Latitude, Longitude, and Time Calculations Practice Questions — JAMB UTME

Question 1Question →

City A is situated at longitude $15^\circ\text{E}$ where the local time is 1:00 PM. What is the local time at City B, located at longitude $60^\circ\text{E}$ ?

10:00 AM

2:00 PM

4:00 PM

5:00 PM

Show answer & explanation

Answer: 4:00 PM

Answer

4:00 PM

The difference in longitude between

15^\circ\text{E}

and

60^\circ\text{E}

is

45^\circ

. Since

15^\circ

of longitude corresponds to 1 hour of time difference,

45^\circ

equals 3 hours (

45 \div 15 = 3

). Because City B lies further east than City A, time is ahead. Adding 3 hours to 1:00 PM yields 4:00 PM.

Step-by-Step Solution

1

Calculate the difference in longitude between the two locations

60^\circ\text{E} - 15^\circ\text{E} = 45^\circ

Both locations are in the Eastern Hemisphere, so subtract the smaller longitude from the larger longitude.

2

Convert the angular difference into time difference

45^\circ \div 15^\circ\text{ per hour} = 3\text{ hours}

The Earth rotates

15^\circ

in 1 hour (

360^\circ

in 24 hours).

3

Adjust local time based on direction of movement

1:00 PM

+ 3\text{ hours} = 4:00\text{ PM}

Eastward movement results in time gain (East-Gain, West-Loss), so add the time difference to the known time.

Key Concept

Longitude and Time Difference Calculation

Question 2Question →

A radio broadcast originates live from City A, located at longitude $10^\circ\text{W}$ , at 09:00 AM local time. What is the local time (expressed as an integer in 24-hour clock format, e.g., 14 for 14:00) at City B, located at longitude $65^\circ\text{E}$ , when the transmission begins?

Show answer & explanation

Answer: 14

Answer

14

City A (

10^\circ\text{W}

) and City B (

65^\circ\text{E}

) have a total angular separation of

75^\circ

. At the rate of

15^\circ

per hour, this equals a 5-hour time difference. Because City B is located to the east of City A, its local time is ahead, so 5 hours added to 09:00 AM gives 14:00 (14).

Step-by-Step Solution

1

Calculate the angular separation between the two longitudes

75^\circ

Since the points lie in different hemispheres (West and East), their longitudinal values must be added together (

10^\circ + 65^\circ = 75^\circ

).

2

Convert angular distance to time difference

5 hours

The Earth rotates

360^\circ

in 24 hours, which equals

15^\circ

per hour (

75^\circ \div 15^\circ = 5\text{ hours}

).

3

Adjust time for directional displacement

14

Travelling eastwards means gaining time because eastern locations experience solar movement earlier. Adding 5 hours to 09:00 AM yields 14:00.

Key Concept

Calculating local time difference across prime meridian boundaries

Question 3Question →

Two meteorological observatories, Station Alpha located at longitude $25^\circ\text{E}$ and Station Beta located in the Western Hemisphere, measure solar illumination simultaneously. When the local solar time at Station Alpha is 4:30 PM, the local solar time at Station Beta is 11:30 AM on the same day. What is the numerical value of the longitude of Station Beta in degrees West?

Show answer & explanation

Answer: 50

Answer

The longitude of Station Beta is

50^\circ\text{W}

.

Station Alpha is at longitude

25^\circ\text{E}

with local solar time 4:30 PM (16:30). Station Beta records a local solar time of 11:30 AM (11:30) on the same day. The time difference is

16:30 - 11:30 = 5\text{ hours}

. Since Earth rotates

15^\circ

per hour, a 5-hour time difference corresponds to an angular distance of

5 \times 15^\circ = 75^\circ

. Because Station Beta's local time is earlier than Station Alpha's local time, Station Beta is located to the west of Station Alpha. Subtracting

25^\circ

to reach the Prime Meridian (

0^\circ

) leaves

50^\circ

west, placing Station Beta at

50^\circ\text{W}

.

Step-by-Step Solution

1

Determine the time difference between the two stations.

Time difference = 16:30 (4:30 PM) - 11:30 (11:30 AM) = 5 hours.

Calculating time separation is the first step in finding angular longitudinal separation.

2

Convert the time difference to angular longitudinal distance using Earth's rotation rate (

15^\circ

per hour).

Angular distance =

5\text{ hours} \times 15^\circ/\text{hour} = 75^\circ

.

The Earth rotates

360^\circ

in 24 hours, which equals

15^\circ

per hour.

3

Determine the relative direction of Station Beta from Station Alpha.

Station Beta is west of Station Alpha.

Places located further west have earlier local times than places further east.

4

Compute the longitude of Station Beta relative to the Prime Meridian (

0^\circ

).

Longitude =

75^\circ - 25^\circ\text{E} = 50^\circ\text{W}

.

Moving

25^\circ

west from

25^\circ\text{E}

reaches

0^\circ

, and the remaining

50^\circ

extends west into the Western Hemisphere.

Key Concept

Calculating longitudinal position from local solar time difference across the Prime Meridian

Question 4Question →

An international news broadcast takes place at $8:00\text{ PM}$ local time in Town X, located at longitude $30^\circ\text{E}$ . What is the local time in Town Y, located at longitude $45^\circ\text{W}$ ?

3:00 PM

1:00 AM the next day

7:00 PM

9:00 PM

Show answer & explanation

Answer: 3:00 PM

Answer

3:00 PM

Because Town X (

30^\circ\text{E}

) and Town Y (

45^\circ\text{W}

) are in opposite hemispheres, their angular separation is

30^\circ + 45^\circ = 75^\circ

. Dividing by

15^\circ

per hour yields a time difference of

5\text{ hours}

. Since Town Y is west of Town X, subtracting 5 hours from

8:00\text{ PM}

correctly gives

3:00\text{ PM}

.

Step-by-Step Solution

1

Calculate the total angular distance between the two longitudes

Since Town X (

30^\circ\text{E}

) and Town Y (

45^\circ\text{W}

) are in different hemispheres (East and West), add their longitudes:

30^\circ + 45^\circ = 75^\circ

.

Locations in opposite hemispheres require adding longitudes to determine total angular separation.

2

Convert the angular distance into a time difference

75^\circ \div 15^\circ/\text{hour} = 5\text{ hours}

.

The Earth rotates

360^\circ

in 24 hours, which rate equals

15^\circ

per hour.

3

Determine the directional adjustment and calculate the target local time

Town Y (

45^\circ\text{W}

) is west of Town X (

30^\circ\text{E}

), so subtract

5\text{ hours}

from

8:00\text{ PM}

(

20:00

):

20:00 - 5\text{ hours} = 15:00

, which is

3:00\text{ PM}

.

Time is behind (earlier) as one travels westward.

Key Concept

Calculating Time Differences Across Hemispheres

Estimated Time:1m 30s

Question 5Question →

A satellite communication signal is transmitted from a ground station located at longitude $40^\circ\text{E}$ at 04:30 PM local time. If the signal is received instantaneously at a tracking station located at longitude $20^\circ\text{W}$ , what is the local solar time at the tracking station at that exact moment?

12:30 PM

08:30 PM

03:10 PM

05:50 PM

Show answer & explanation

Answer: 12:30 PM

Answer

12:30 PM

To find the local time at

20^\circ\text{W}

, add the longitudes because they are in opposite hemispheres (

40^\circ\text{E} + 20^\circ\text{W} = 60^\circ

). Convert the angular distance to time (

60^\circ \div 15^\circ = 4\text{ hours}

). Because the receiving station is located to the west of the transmitting station, subtract 4 hours from 04:30 PM, obtaining 12:30 PM.

Step-by-Step Solution

1

Calculate total longitudinal distance between the two locations.

Longitudinal difference =

40^\circ\text{E} + 20^\circ\text{W} = 60^\circ

.

Locations in opposite hemispheres (East and West) require adding their longitudinal values to find total angular distance.

2

Convert the longitudinal difference into a time difference.

Time difference =

\frac{60^\circ}{15^\circ/\text{hour}} = 4\text{ hours}

.

The Earth rotates

360^\circ

in 24 hours, which corresponds to

15^\circ

per hour.

3

Determine whether to add or subtract time based on direction.

Local time at

20^\circ\text{W} = 04:30\text{ PM} - 4\text{ hours} = 12:30\text{ PM}

.

Locations to the west are behind in local solar time compared to locations to the east.

Key Concept

Calculation of local solar time differences across meridians in opposite hemispheres

Estimated Time:1m 30s

Question 6Question →

An airplane departs from Town X, located at longitude $45^\circ\text{E}$ , at 08:30 local time on Tuesday, bound for Town Y, located at longitude $75^\circ\text{W}$ . If the total flight duration is 10 hours, what is the local time and day of arrival at Town Y?

10:30 AM on Tuesday

02:30 AM on Wednesday

04:30 PM on Tuesday

12:30 AM on Tuesday

Show answer & explanation

Answer: 10:30 AM on Tuesday

Answer

10:30 AM on Tuesday

The correct arrival time is 10:30 AM on Tuesday. Because Town X (

45^\circ\text{E}

) and Town Y (

75^\circ\text{W}

) are in different hemispheres, their longitudinal distance is

45^\circ + 75^\circ = 120^\circ

. Dividing by

15^\circ

per hour gives an 8-hour time difference. Since Town Y lies west of Town X, time is subtracted, making the local time at Town Y at the moment of departure 00:30 (12:30 AM) on Tuesday. Adding the 10-hour flight time results in arrival at 10:30 AM on Tuesday.

Step-by-Step Solution

1

Calculate total longitudinal difference between Town X (

45^\circ\text{E}

) and Town Y (

75^\circ\text{W}

).

45^\circ + 75^\circ = 120^\circ

longitudinal difference.

Locations in opposite hemispheres (East and West) require adding longitudes to find total angular separation.

2

Convert longitudinal difference into time difference using

15^\circ = 1\text{ hour}

.

\frac{120^\circ}{15^\circ} = 8\text{ hours}

time difference.

Earth rotates

360^\circ

in 24 hours, which equals

15^\circ

per hour.

3

Determine local departure time at Town Y.

08:30 - 8\text{ hours} = 00:30\text{ (12:30 AM) on Tuesday}

.

Town Y is west of Town X, so local time is behind (subtract time when moving west).

4

Add the flight duration to the local departure time at Town Y.

00:30 + 10\text{ hours} = 10:30\text{ AM on Tuesday}

.

Elapsed flight time moves local arrival time forward by 10 hours.

Key Concept

Longitude and local time adjustment across meridians and flight duration

Estimated Time:2m 0s

Question 7Question →

If the local time at the Greenwich Meridian ( $0^\circ$ ) is 12:00 noon, what is the longitude of a city where the local time is 4:00 PM on the same day? Express your answer as a number in degrees East.

Show answer & explanation

Answer: 60

Answer

The longitude of the city is

60^\circ\text{E}

.

The time difference between 12:00 noon and 4:00 PM is 4 hours. Since the Earth rotates

15^\circ

per hour, 4 hours corresponds to

4 \times 15^\circ = 60^\circ

. Because the local time at the city is ahead of Greenwich Mean Time (GMT), the city lies to the East of the Greenwich Meridian at longitude

60^\circ\text{E}

.

Step-by-Step Solution

1

Determine the time difference between the two locations.

Time difference = 4 hours

Subtract 12:00 noon from 4:00 PM (16:00).

2

Convert the time difference into degrees of longitude.

Angular distance =

60^\circ

Earth rotates

360^\circ

in 24 hours, which equals

15^\circ

per hour (

4\text{ hours} \times 15^\circ = 60^\circ

).

3

Determine the direction (East or West) relative to the Prime Meridian.

60^\circ\text{E}

Locations with time ahead of Greenwich are to the East.

Key Concept

Calculation of longitude from local time difference relative to Greenwich Meridian

Question 8Question →

A navigator on Ship P observes local solar noon (12:00 noon) when a Greenwich Mean Time (GMT) chronometer reads 1:40 PM. If Ship Q is located at a position where the local time is exactly 4 hours ahead of Ship P, what is the longitude of Ship Q?

35^\circ\text{E}

35^\circ\text{W}

85^\circ\text{E}

85^\circ\text{W}

Show answer & explanation

Answer: $35^\circ\text{E}$

Answer

35^\circ\text{E}

Ship P is at

25^\circ\text{W}

because its local time is 1 hour 40 minutes (100 minutes) behind GMT (100 minutes / 4 min per degree =

25^\circ\text{W}

). Since Ship Q is 4 hours ahead in time, it lies

60^\circ

to the east (

4 \times 15^\circ

). Measuring

60^\circ

east from

25^\circ\text{W}

covers

25^\circ

to reach the Greenwich Meridian (

0^\circ

), leaving

35^\circ

into the Eastern Hemisphere, resulting in

35^\circ\text{E}

.

Step-by-Step Solution

1

Calculate the longitude of Ship P using local time and GMT

Time difference = 1 hour 40 minutes = 100 minutes. Longitude of Ship P =

100 \text{ minutes} / 4 \text{ minutes per degree} = 25^\circ\text{W}

(since local time is behind GMT).

The Earth rotates

1^\circ

every 4 minutes, and areas behind GMT are located in the Western Hemisphere.

2

Determine the time difference and direction from Ship P to Ship Q

Time difference = 4 hours ahead. Direction = East of Ship P.

Local time increases as one moves east.

3

Convert the 4-hour time difference into angular distance in degrees

Angular distance =

4 \text{ hours} \times 15^\circ/\text{hour} = 60^\circ

.

Earth rotates at a rate of

15^\circ

per hour.

4

Calculate the longitude of Ship Q by moving

60^\circ

east from

25^\circ\text{W}

Distance to Greenwich Meridian (

0^\circ

) =

25^\circ

east. Remaining distance east into Eastern Hemisphere =

60^\circ - 25^\circ = 35^\circ\text{E}

.

Crossing the Prime Meridian changes the hemisphere designation from West to East.

Key Concept

Longitude calculation using Greenwich Mean Time (GMT) and local time adjustments across meridians

Estimated Time:2m 0s

Question 9Question →

A solar observation station located at longitude $23^\circ\text{W}$ records local solar noon ( $12:00\text{ PM}$ ) at a specific instant. At that exact moment, a research vessel at sea notes its local solar time as $7:16\text{ PM}$ ( $19:16$ ) on the same day. What is the longitude of the research vessel in degrees East?

Show answer & explanation

Answer: 86

Answer

The research vessel is located at

86^\circ\text{E}

.

The time difference between 12:00 PM and 7:16 PM is 7 hours and 16 minutes (436 minutes). Since 4 minutes correspond to 1° of longitude, the angular difference is 436 ÷ 4 = 109°. Because the vessel's solar time is later than the station's time, the vessel lies to the East. Moving 109° East from 23°W requires 23° to reach the 0° Greenwich Meridian and an additional 86° into the Eastern Hemisphere, placing the vessel at 86°E.

Step-by-Step Solution

1

Determine the time difference between the solar observation station and the research vessel.

Time difference = 19:16 - 12:00 = 7 hours and 16 minutes = 436 minutes.

Difference in local solar time corresponds to longitudinal separation.

2

Convert the time difference into longitudinal degrees using the rate of Earth's rotation (

1^\circ = 4\text{ minutes}

).

Longitudinal difference = 436 ÷ 4 = 109°.

The Earth rotates 360° in 24 hours, which equals 1° for every 4 minutes of time difference.

3

Determine the direction of the vessel relative to the station.

The vessel is East of the station.

Local solar time at the vessel (7:16 PM) is ahead of the station (12:00 PM), meaning the vessel lies further East.

4

Calculate the absolute longitude in the Eastern Hemisphere.

Vessel longitude = 109° - 23° = 86°E.

Traversing 109° East starting from 23°W uses 23° to reach the Greenwich Meridian (0°) and the remaining 86° extends into the Eastern Hemisphere.

Key Concept

Calculating longitude from local solar time difference across meridians

Question 10Question →

A ship captain at sea observes local solar noon ( $12:00\text{ PM}$ ) on Monday. At that precise moment, a radio time signal from Greenwich ( $0^\circ$ ) indicates that Greenwich Mean Time (GMT) is $05:20\text{ PM}$ on Monday. What is the longitude of the ship in degrees West of the Prime Meridian?

Show answer & explanation

Answer: 80

Answer

The longitude of the ship is

80^\circ\text{W}

(80 degrees West).

The time difference between local solar noon (

12:00\text{ PM}

) and GMT (

05:20\text{ PM}

) is 5 hours and 20 minutes, or

5\frac{1}{3}

hours. Multiplying

5.333\text{ hours}

by

15^\circ

per hour yields

80^\circ

. Since local solar time is behind GMT, the ship is situated

80^\circ

West of the Prime Meridian.

Step-by-Step Solution

1

Calculate the time difference between local solar time and Greenwich Mean Time (GMT)

05:20\text{ PM} - 12:00\text{ PM} = 5\text{ hours and } 20\text{ minutes} = 5.333\text{ hours}

The distance in longitude is directly proportional to the difference between local time and GMT.

2

Convert the time difference into angular distance in degrees of longitude

5\frac{1}{3}\text{ hours} \times 15^\circ/\text{hour} = 80^\circ

Earth rotates

360^\circ

in 24 hours, which corresponds to

15^\circ

of longitude for every 1 hour of time difference.

3

Determine hemisphere direction based on whether local time is ahead or behind GMT

Western Hemisphere (

80^\circ\text{W}

)

Local time (

12:00\text{ PM}

) is earlier than GMT (

05:20\text{ PM}

), placing the ship west of the Prime Meridian.

Key Concept

Calculating longitude using local time and Greenwich Mean Time (GMT)

Question 11Question →

A weather monitoring station situated at longitude $55^\circ\text{W}$ records a local solar time of $08:20\text{ AM}$ . At the exact same instant, a maritime research vessel logs a local solar time of $02:40\text{ PM}$ . What is the longitude of the maritime research vessel in degrees East ( $^\circ\text{E}$ )?

Show answer & explanation

Answer: 40

Answer

The longitude of the maritime research vessel is

40^\circ\text{E}

.

The time difference between

08:20\text{ AM}

(

55^\circ\text{W}

) and

02:40\text{ PM}

(

14:40

) is

6\text{ hours and } 20\text{ minutes}

, which equals

380\text{ minutes}

. At a rate of

4\text{ minutes per degree}

of longitude, this represents a longitudinal difference of

95^\circ

. Since the vessel's local solar time is ahead, it is situated to the East. Measuring

95^\circ

East from

55^\circ\text{W}

crosses the Greenwich Meridian (

0^\circ

) after

55^\circ

, placing the vessel at

40^\circ\text{E}

.

Step-by-Step Solution

1

Calculate the time difference between the weather monitoring station and the maritime research vessel.

Time difference =

14:40 - 08:20 = 6\text{ hours } 20\text{ minutes} = 380\text{ minutes}

.

Converting 02:40 PM to 24-hour solar time (14:40) allows direct subtraction of the times.

2

Convert the time difference into angular degrees of longitude.

Angular distance =

\frac{380\text{ minutes}}{4\text{ minutes per degree}} = 95^\circ

.

The Earth rotates

360^\circ

in 24 hours, which corresponds to

1^\circ

of longitude every 4 minutes.

3

Determine the direction and calculate the vessel's longitude.

95^\circ\text{ East} - 55^\circ\text{ West to Prime Meridian} = 40^\circ\text{E}

.

Because the local solar time at the vessel is ahead (later in the day), the vessel is located to the East. Traveling

95^\circ

East starting from

55^\circ\text{W}

uses

55^\circ

to reach

0^\circ

(Prime Meridian), leaving

40^\circ

in the Eastern Hemisphere.

Key Concept

Longitude calculation from local solar time difference across the Prime Meridian

Estimated Time:1m 30s

Question 12Question →

City X is located at longitude $15^\circ\text{E}$ . When the local time at City X is $2:00\text{ PM}$ , what is the local time at City Y, located at longitude $45^\circ\text{E}$ ?

4:00\text{ PM}

12:00\text{ noon}

3:00\text{ PM}

1:00\text{ PM}

Show answer & explanation

Answer: $4:00\text{ PM}$

Answer

The local time at City Y is

4:00\text{ PM}

.

The difference in longitude between City X (

15^\circ\text{E}

) and City Y (

45^\circ\text{E}

) is

30^\circ

. Since

15^\circ

corresponds to 1 hour,

30^\circ

equals 2 hours. Because City Y lies to the east of City X, local time is ahead, so 2 hours must be added to

2:00\text{ PM}

, giving

4:00\text{ PM}

.

Step-by-Step Solution

1

Calculate the angular longitudinal difference between City X and City Y.

Difference

= 45^\circ\text{E} - 15^\circ\text{E} = 30^\circ

.

Since both cities are in the Eastern Hemisphere, subtract the smaller longitude from the larger longitude.

2

Convert the longitudinal difference into a time difference.

Time difference

= 30^\circ \div 15^\circ/\text{hour} = 2\text{ hours}

.

The Earth rotates

15^\circ

per hour (

360^\circ

in 24 hours).

3

Determine whether to add or subtract the time difference.

Local time

= 2:00\text{ PM} + 2\text{ hours} = 4:00\text{ PM}

.

City Y (

45^\circ\text{E}

) is east of City X (

15^\circ\text{E}

), so time is ahead (gain time going east).

Key Concept

Calculation of local time difference using longitudinal intervals

Estimated Time:45s

Question 13Question →

A solar eclipse reaches maximum totality in Town P, located at longitude $15^\circ\text{W}$ , at $11:20\text{ AM}$ local time. What is the local time in Town Q, located at longitude $45^\circ\text{E}$ , at that exact moment?

3:20\text{ PM}

7:20\text{ AM}

1:20\text{ PM}

9:20\text{ AM}

Show answer & explanation

Answer: $3:20\text{ PM}$

Answer

The local time in Town Q is

3:20\text{ PM}

.

Because Town P (

15^\circ\text{W}

) and Town Q (

45^\circ\text{E}

) are in opposite hemispheres, the total longitudinal distance between them is

15^\circ + 45^\circ = 60^\circ

. Since

15^\circ

equals

1

hour of time difference,

60^\circ

equals

4

hours. Because Town Q is situated east of Town P, time is ahead in Town Q. Adding

4

hours to

11:20\text{ AM}

yields

3:20\text{ PM}

.

Step-by-Step Solution

1

Calculate the total longitudinal difference between Town P (

15^\circ\text{W}

) and Town Q (

45^\circ\text{E}

).

Longitudinal difference

= 15^\circ + 45^\circ = 60^\circ

.

Since the towns are in opposite hemispheres (West and East), their longitudes are added to find the total angular distance.

2

Convert the longitudinal difference into time.

Time difference

= 60^\circ \div 15^\circ/\text{hour} = 4\text{ hours}

.

The Earth rotates

15^\circ

per hour (

1^\circ

every

4

minutes).

3

Determine the time in Town Q relative to Town P.

Local time in Town Q

= 11:20\text{ AM} + 4\text{ hours} = 3:20\text{ PM}

.

Town Q lies to the east of Town P, so its time is ahead of Town P's local time.

Key Concept

Longitude and Time Calculations Across Meridians

Estimated Time:1m 30s

Question 14Question →

Town P is located at longitude $60^\circ\text{E}$ , where the local solar time is $12:00\text{ noon}$ . Town Q is located at longitude $15^\circ\text{W}$ . What is the local solar time at Town Q, expressed as the hour of the day in 24-hour time?

Show answer & explanation

Answer: 7

Answer

The local solar time at Town Q is 7:00 (represented by the number 7).

To find the local time at Town Q (

15^\circ\text{W}

) relative to Town P (

60^\circ\text{E}

at

12:00\text{ noon}

), calculate the longitudinal distance:

60^\circ + 15^\circ = 75^\circ

. Dividing by

15^\circ

per hour gives a time difference of

5\text{ hours}

. Because Town Q is west of Town P, subtract 5 hours from 12:00 to obtain 7:00 (

7

).

Step-by-Step Solution

1

Calculate the longitudinal difference between Town P and Town Q.

Total angular separation =

60^\circ\text{E} + 15^\circ\text{W} = 75^\circ

.

Locations in opposite hemispheres (East and West) require adding their longitude values to determine total angular distance.

2

Convert the angular distance into hours.

Time difference =

75^\circ \div 15^\circ/\text{hour} = 5\text{ hours}

.

Earth rotates

360^\circ

in 24 hours, which corresponds to

15^\circ

per hour.

3

Adjust time based on relative position.

Local time at Town Q =

12:00 - 5\text{ hours} = 7:00

(

7

).

Town Q lies to the west of Town P, so its local time is behind that of Town P.

Key Concept

Calculating local solar time across different longitudes in opposite hemispheres.

Question 15Question →

A research station located at longitude $142^\circ\text{E}$ records a solar flare observation at $03:16\text{ PM}$ local solar time. At the exact same instant, an oceanographic vessel records the same solar flare at $07:48\text{ AM}$ local solar time on the same day. What is the longitude of the oceanographic vessel in degrees East?

Show answer & explanation

Answer: 30

Answer

The longitude of the oceanographic vessel is

30^\circ\text{E}

.

The research station's local solar time is 15:16 and the oceanographic vessel's time is 07:48, giving a difference of 7 hours 28 minutes (448 minutes). Since

1^\circ

of longitude corresponds to 4 minutes of time, the longitudinal difference is

448 \div 4 = 112^\circ

. Because the vessel's local solar time is earlier than that of the research station, the vessel is located to the west of the research station (

142^\circ\text{E} - 112^\circ = 30^\circ\text{E}

).

Step-by-Step Solution

1

Convert both local solar times to 24-hour time format and subtract to determine the exact time difference

Research station time = 15:16, Vessel time = 07:48. Time difference = 7 hours 28 minutes (448 minutes).

Converting to 24-hour format simplifies direct subtraction to evaluate the total time delta between the two locations.

2

Convert the total time difference in minutes to angular longitudinal distance

448 minutes ÷ 4 minutes per degree = 112° difference in longitude.

Earth rotates 360° in 24 hours (1440 minutes), establishing a rate of 1° longitude change per 4 minutes of local time difference.

3

Evaluate direction of location and subtract angular distance from the station's longitude

Vessel time is behind station time, placing it west of the station: 142°E - 112° = 30°E.

Places located further west experience earlier local solar time. Subtracting 112° from 142°E yields 30°E.

Key Concept

Longitude and Time Calculations (converting solar time difference to longitudinal angular distance)

Question 16Question →

An aircraft departs from City A located at longitude $35^\circ\text{W}$ at $08:45\text{ AM}$ local time on Tuesday for a non-stop flight to City B located at longitude $105^\circ\text{E}$ . If the total flight duration is 14 hours and 30 minutes, what is the local time and day of arrival at City B?

08:35\text{ AM}

on Wednesday

01:55\text{ PM}

on Tuesday

03:55\text{ AM}

on Wednesday

08:35\text{ PM}

on Tuesday

Show answer & explanation

Answer: $08:35\text{ AM}$ on Wednesday

Answer

08:35\text{ AM}

on Wednesday

The longitudinal difference between

35^\circ\text{W}

and

105^\circ\text{E}

is

140^\circ

, equivalent to a 9-hour 20-minute time difference. Since City B is east of City A, its time is ahead by 9 hours and 20 minutes, giving a local departure time at City B of

06:05\text{ PM}

Tuesday. Adding the 14-hour 30-minute flight duration brings the time to

08:35\text{ AM}

on Wednesday.

Step-by-Step Solution

1

Calculate the total longitudinal difference between City A (

35^\circ\text{W}

) and City B (

105^\circ\text{E}

).

\text{Longitude difference} = 35^\circ + 105^\circ = 140^\circ

Because the two places are in opposite hemispheres (West and East), their longitudinal values must be added.

2

Convert the longitudinal difference into a time difference.

140^\circ \times 4\text{ minutes/degree} = 560\text{ minutes} = 9\text{ hours and } 20\text{ minutes}

Earth rotates

1^\circ

every 4 minutes.

3

Determine the local time at City B when the flight departs from City A.

08:45\text{ AM} + 9\text{ hours } 20\text{ minutes} = 06:05\text{ PM}\text{ (or } 18:05\text{)} \text{ on Tuesday}

Places to the East are ahead in time, so the time difference must be added to City A's departure time.

4

Add the flight duration to City B's departure time to find arrival time and day.

18:05 + 14\text{ hours } 30\text{ minutes} = 32:35 \Rightarrow 08:35\text{ AM} \text{ on Wednesday}

32:35

represents 8 hours and 35 minutes past midnight, which advances the calendar date by one day from Tuesday to Wednesday.

Key Concept

Calculation of time differences across eastern and western hemispheres considering flight duration and day change

Question 17Question →

Town A is situated at longitude $20^\circ\text{W}$ . When the local solar time at Town A is $09:00\text{ AM}$ , the local solar time at Town B is $01:00\text{ PM}$ on the same day. What is the longitude of Town B in degrees East?

Show answer & explanation

Answer: 40

Answer

The longitude of Town B is 40°E.

Town B is 4 hours ahead of Town A, which corresponds to an angular distance of

60^\circ

East (

4 \times 15^\circ

). Traveling

60^\circ

East starting from

20^\circ\text{W}

takes

20^\circ

to reach the Prime Meridian (

0^\circ

), and the remaining

40^\circ

places Town B at

40^\circ\text{E}

.

Step-by-Step Solution

1

Calculate the difference in local solar time between Town A and Town B.

Time difference =

13:00 - 09:00 = 4\text{ hours}

.

Local solar time differences represent angular distance between meridians.

2

Convert the time difference into degrees of longitude.

4\text{ hours} \times 15^\circ/\text{hour} = 60^\circ

longitude difference.

The Earth rotates

360^\circ

in 24 hours, which corresponds to

15^\circ

of longitude per hour.

3

Determine direction and calculate the exact longitude of Town B.

Moving

60^\circ

East from

20^\circ\text{W}

gives

40^\circ\text{E}

.

Because Town B has a later time, it lies to the East. Subtracting

20^\circ

reaches the Prime Meridian (

0^\circ

), leaving

40^\circ

in the Eastern Hemisphere.

Key Concept

Calculating Longitude from Local Solar Time Differences Across Meridians

Estimated Time:1m 30s

Question 18Question →

A radio signal transmitted live from Station X, located at longitude $78^\circ\text{E}$ , is logged at $10:40\text{ AM}$ local solar time. At the exact same instant, the signal is received at Station Y, where the local solar time is logged as $03:16\text{ PM}$ on the same day. What is the longitude of Station Y in degrees East?

Show answer & explanation

Answer: 147

Answer

147°E

The time difference between 10:40 AM and 03:16 PM is 4 hours and 36 minutes. Converting this time difference to degrees using

15^\circ

per hour (

4 \times 15^\circ = 60^\circ

) and

1^\circ

per 4 minutes (

36 \text{ min} / 4 \text{ min/degree} = 9^\circ

) gives a total longitudinal distance of

69^\circ

. Because Station Y has a later solar time than Station X, it is situated further East. Adding

69^\circ

to

78^\circ\text{E}

yields

147^\circ\text{E}

.

Step-by-Step Solution

1

Calculate the time difference between Station Y and Station X

4 hours and 36 minutes

Subtracting the earlier local time at Station X (10:40 AM) from the later local time at Station Y (03:16 PM) yields a duration of 4 hours and 36 minutes.

2

Convert the calculated time difference into longitudinal degrees

69 degrees

Earth rotates through 15° of longitude per hour (or 1° every 4 minutes). Thus, 4 hours corresponds to 60° and 36 minutes corresponds to 9°, giving a total of 69°.

3

Calculate the longitude of Station Y based on directional time relationship

147°E

Because local time at Station Y is later than at Station X, Station Y lies further East. Adding the angular separation of 69° to 78°E results in 147°E.

Key Concept

Longitude calculation from local time difference

Question 19Question →

Two weather observation stations, Station A and Station B, record simultaneous solar observations. Station A is located at longitude $12^\circ\text{W}$ where the local solar time is $02:00\text{ PM}$ . At the exact same moment, the local solar time at Station B is $07:00\text{ PM}$ . What is the longitude of Station B in degrees East ( $^\circ\text{E}$ )?

Show answer & explanation

Answer: 63

Answer

The longitude of Station B is

63^\circ\text{E}

.

The local time difference between Station A (

02:00\text{ PM}

) and Station B (

07:00\text{ PM}

) is

5\text{ hours}

. Since

1\text{ hour}

equals

15^\circ

of longitude, a

5\text{-hour}

difference equals

75^\circ

of angular distance (

5 \times 15^\circ

). Station B's local time is ahead of Station A, indicating that Station B is located further East. Starting from

12^\circ\text{W}

and moving

75^\circ

East,

12^\circ

is required to reach

0^\circ

(the Prime Meridian), leaving

63^\circ

into the Eastern Hemisphere. Therefore, Station B is located at

63^\circ\text{E}

.

Step-by-Step Solution

1

Calculate the time difference between Station A and Station B.

Station B (

19:00

) is

5\text{ hours}

ahead of Station A (

14:00

).

Comparing local solar times gives the time separation between the two longitudes.

2

Convert the time difference into angular distance in degrees.

5\text{ hours} \times 15^\circ/\text{hour} = 75^\circ

angular distance.

The Earth rotates

360^\circ

in 24 hours, which corresponds to

15^\circ

of longitude per hour.

3

Determine the longitude of Station B from Station A across the Prime Meridian.

75^\circ\text{ East} - 12^\circ\text{W} = 63^\circ\text{E}

.

Station B is later in solar time, so it lies East of Station A. Moving East from

12^\circ\text{W}

uses

12^\circ

to reach

0^\circ

(Prime Meridian) and the remaining

63^\circ

enters the Eastern Hemisphere.

Key Concept

Calculating longitude from local time difference across meridians

Estimated Time:1m 30s

Question 20Question →

Two meteorological stations are situated along different meridians. Station Alpha is positioned at longitude $38^\circ\text{W}$ , while Station Beta is positioned at longitude $82^\circ\text{E}$ . What is the difference in local solar time between these two stations, in hours?

Show answer & explanation

Answer: 8

Answer

The difference in local solar time between the two stations is 8 hours.

Station Alpha is located in the Western Hemisphere (

38^\circ\text{W}

) and Station Beta is located in the Eastern Hemisphere (

82^\circ\text{E}

). The total angular distance separating them across the Greenwich Meridian is

38^\circ + 82^\circ = 120^\circ

. Dividing

120^\circ

by the Earth's rotation speed of

15^\circ

per hour gives a time difference of 8 hours.

Step-by-Step Solution

1

Calculate the total longitudinal angular distance between

38^\circ\text{W}

and

82^\circ\text{E}

.

Angular distance =

38^\circ + 82^\circ = 120^\circ

.

Because the two locations lie in opposite hemispheres relative to the Prime Meridian (

0^\circ

), their longitudinal degree values must be added together.

2

Convert the total angular distance to time difference in hours.

Time difference =

120^\circ \div 15^\circ\text{/hour} = 8\text{ hours}

.

The Earth completes a

360^\circ

rotation in 24 hours, which corresponds to

15^\circ

per hour.

Key Concept

Calculation of longitudinal difference across the Prime Meridian and conversion to local solar time difference.

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