Time, Rate, and Distance Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 2

Soru 21Soru →

A dispatch rider is transporting urgent documents between two military installations. The rider travels on a paved highway at a constant speed of $65\text{ mph}$ for $1\text{ hour and } 12\text{ minutes}$ . Upon reaching a rural sector, the rider continues on an unpaved route at a steady speed of $42\text{ mph}$ for $35\text{ minutes}$ . What is the total distance, in miles, the dispatch rider traveled?

Cevabı ve açıklamayı göster

Cevap: 102.5

Cevap

102.5

To find the total distance, calculate the distance for each leg of the trip separately by ensuring time is expressed in hours. For the first leg,

1\text{ hour and } 12\text{ minutes}

is

1.2\text{ hours}

. Multiplying the

65\text{ mph}

rate by

1.2\text{ hours}

gives

78\text{ miles}

. For the second leg,

35\text{ minutes}

is

\frac{35}{60}

or

\frac{7}{12}\text{ of an hour}

. Multiplying the

42\text{ mph}

rate by

\frac{7}{12}\text{ hours}

gives

24.5\text{ miles}

. Adding these two distances together (

78 + 24.5

) gives a total of

102.5\text{ miles}

.

Adım Adım Çözüm

1

Convert the highway travel time into hours.

1\text{ hour and } 12\text{ minutes} = 1 + \frac{12}{60}\text{ hours} = 1.2\text{ hours}

.

The speed is given in miles per hour, so time must be converted to hours to match units.

2

Calculate the distance traveled on the highway.

65\text{ mph} \times 1.2\text{ hours} = 78\text{ miles}

.

Applying the formula: Distance = Rate

\times

Time.

3

Convert the unpaved route travel time into hours.

35\text{ minutes} = \frac{35}{60}\text{ hours} = \frac{7}{12}\text{ hours}

.

Time must be in hours for consistency with the speed unit.

4

Calculate the distance traveled on the unpaved route.

42\text{ mph} \times \frac{7}{12}\text{ hours} = 24.5\text{ miles}

.

Applying the formula: Distance = Rate

\times

Time.

5

Calculate the total distance.

78\text{ miles} + 24.5\text{ miles} = 102.5\text{ miles}

.

The total journey distance is the sum of the individual distances from each leg.

Anahtar Kavram

Calculating total distance for a multi-leg journey by accurately converting fractional times to hours and applying the distance formula.

Soru 22Soru →

A disaster relief team is transporting supplies to a stricken area. They first drive their trucks on a paved highway at a constant speed of $52\text{ miles per hour}$ for $1\text{ hour and } 15\text{ minutes}$ . They then transition to rough off-road terrain, where they travel at a steady speed of $18\text{ miles per hour}$ for $40\text{ minutes}$ to reach their final destination. What is the total distance traveled by the team?

65\text{ miles}

67\text{ miles}

77\text{ miles}

4,620\text{ miles}

Cevabı ve açıklamayı göster

Cevap: $77\text{ miles}$

Cevap

The correct total distance is

77\text{ miles}

.

The total distance is the sum of the distances from both legs of the trip. The first leg is 1 hour and 15 minutes (1.25 hours) at 52 mph, which equals 65 miles. The second leg is 40 minutes (2/3 of an hour) at 18 mph, which equals 12 miles. Adding these gives a total of 77 miles.

Adım Adım Çözüm

1

Convert the travel time for the first leg into hours.

1\text{ hour and } 15\text{ minutes} = 1\frac{15}{60}\text{ hours} = 1.25\text{ hours}

.

Speed is given in miles per hour, so time must be converted into hours to correctly calculate the distance.

2

Calculate the distance traveled during the first leg.

52\text{ mph} \times 1.25\text{ hours} = 65\text{ miles}

.

Distance equals rate multiplied by time (

D = R \times T

).

3

Convert the travel time for the second leg into hours.

40\text{ minutes} = \frac{40}{60}\text{ hours} = \frac{2}{3}\text{ hours}

.

Consistent units are required for the second leg's calculation.

4

Calculate the distance traveled during the second leg.

18\text{ mph} \times \frac{2}{3}\text{ hours} = 12\text{ miles}

.

Using the

D = R \times T

formula for the off-road section.

5

Add the distances of both legs to find the total distance.

65\text{ miles} + 12\text{ miles} = 77\text{ miles}

.

The question asks for the total combined distance traveled by the team to reach their destination.

Anahtar Kavram

Calculating total distance for multi-leg journeys by applying the

D = R \times T

formula with necessary time unit conversions.

Tahmini Süre:1m 30s

Soru 23Soru →

A Coast Guard cutter is navigating to a waypoint that is $135$ miles away. If the vessel travels at a steady rate of $30$ miles per hour, how much time will it take to reach the waypoint?

4

hours and

5

minutes

7

hours and

30

minutes

4

hours and

30

minutes

4

hours and

50

minutes

Cevabı ve açıklamayı göster

Cevap: $4$ hours and $30$ minutes

Cevap

The correct answer is

4

hours and

30

minutes.

To find the travel time, divide the total distance by the speed:

135 \div 30 = 4.5

hours. Since

0.5

of an hour is exactly half of

60

minutes, it equals

30

minutes. Thus, the total travel time is

4

hours and

30

minutes.

Adım Adım Çözüm

1

Set up the formula for finding time given distance and rate.

Time = \frac{135}{30}

The standard relationship between distance, rate, and time is

Time = \frac{Distance}{Rate}

.

2

Divide the total distance by the rate to find the time in hours.

135 \div 30 = 4.5

hours

Performing the division gives the total travel time in decimal hours.

3

Convert the decimal portion of the hour into minutes.

0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}

Since the options are presented in hours and minutes, the fractional hour must be converted using the factor of

60

minutes per hour.

Anahtar Kavram

Calculating Time given Rate and Distance

Tahmini Süre:45s

Soru 24Soru →

A naval submarine travels completely submerged at a steady cruising speed of $40\text{ knots}$ . If it maintains this speed for $3\text{ hours and } 15\text{ minutes}$ during a continuous sonar patrol, what is the total distance covered?

120\text{ nautical miles}

126\text{ nautical miles}

130\text{ nautical miles}

720\text{ nautical miles}

Cevabı ve açıklamayı göster

Cevap: $130\text{ nautical miles}$

Cevap

130\text{ nautical miles}

The correct answer is derived by converting the

15\text{ minutes}

into

0.25\text{ hours}

, yielding a total continuous travel time of

3.25\text{ hours}

. Multiplying the cruising speed of

40\text{ knots}

by

3.25\text{ hours}

results in exactly

130\text{ nautical miles}

.

Adım Adım Çözüm

1

Identify the standard distance formula.

\text{Distance} = \text{Rate} \times \text{Time}

This formula connects speed, travel time, and distance covered.

2

Convert the mixed time measurement (

3\text{ hours and } 15\text{ minutes}

) entirely into hours.

15\text{ minutes} \div 60\text{ minutes/hour} = 0.25\text{ hours}

. Total time is

3 + 0.25 = 3.25\text{ hours}

.

The rate is given in knots (nautical miles per hour), so the time must be strictly in hours before multiplication.

3

Multiply the rate by the total time in hours.

40 \times 3.25 = 130\text{ nautical miles}

Applying the values to the distance formula yields the total traveled distance.

Anahtar Kavram

Calculating distance by standardizing mixed time units (hours and minutes) into a single metric before multiplying by rate.

Soru 25Soru →

A military cargo plane needs to transport supplies to a base that is $900$ miles away. If the plane flies at a constant speed of $300$ miles per hour, how many hours will the flight take?

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The flight will take 3 hours.

To find the travel time, the total distance must be divided by the constant rate of speed. By applying the formula

\text{Time} = \frac{\text{Distance}}{\text{Rate}}

, dividing the

900

mile distance by the

300

mile per hour speed yields exactly

3

hours.

Adım Adım Çözüm

1

Identify the known values from the word problem.

\text{Distance} = 900

miles,

\text{Rate} = 300

miles per hour.

These are the two variables required to solve for the missing variable, which is time.

2

Apply the time formula.

\text{Time} = \frac{900}{300} = 3

.

Time is equal to total distance divided by the constant rate.

Anahtar Kavram

Calculating elapsed time using the distance and rate formula.

Tahmini Süre:45s

Soru 26Soru →

A military cargo plane flies from Base Alpha to Base Bravo at a steady cruising speed of $320\text{ miles per hour}$ . This first leg of the flight takes $2\text{ hours and } 45\text{ minutes}$ . After refueling, the plane continues to Base Charlie, flying at $280\text{ miles per hour}$ for $1\text{ hour and } 30\text{ minutes}$ . What is the total distance traveled by the cargo plane from Base Alpha to Base Charlie? Include both the numeric value and unit in your answer (e.g., '500 miles').

Cevabı ve açıklamayı göster

Cevap: 1300 miles; 1,300 miles; 1300 mi; 1300; 1,300

Cevap

1300 miles

The correct answer is found by first converting all travel times into decimal hours. The first leg is

2.75

hours at

320\text{ mph}

, covering

880\text{ miles}

. The second leg is

1.5

hours at

280\text{ mph}

, covering

420\text{ miles}

. Adding these two distances yields a total of

1300\text{ miles}

.

Adım Adım Çözüm

1

Convert the flight times into decimal hours.

2\text{ hours and } 45\text{ minutes} = 2.75\text{ hours}

;

1\text{ hour and } 30\text{ minutes} = 1.5\text{ hours}

.

To calculate distance using miles per hour, the time units must be converted to hours.

2

Calculate the distance for the first leg from Base Alpha to Base Bravo.

320\text{ mph} \times 2.75\text{ hours} = 880\text{ miles}

.

Distance equals rate multiplied by time (

d = r \times t

).

3

Calculate the distance for the second leg from Base Bravo to Base Charlie.

280\text{ mph} \times 1.5\text{ hours} = 420\text{ miles}

.

The second leg must be calculated independently due to the change in both speed and travel time.

4

Add the distances of both legs to find the total distance traveled.

880\text{ miles} + 420\text{ miles} = 1300\text{ miles}

.

The total journey distance is the sum of the distances of all individual legs.

Anahtar Kavram

Calculating multi-leg total distance using

d = r \times t

with unit conversions.

Soru 27Soru →

A surveillance drone flies at a constant speed of $40$ miles per hour. How many minutes will it take the drone to travel a distance of $10$ miles?

15

4

25

0.25

Cevabı ve açıklamayı göster

Cevap: $15$

Cevap

15

minutes

The correct answer is found by dividing the distance (

10

miles) by the speed (

40

miles per hour) to get the time in hours, which is

0.25

hours. Then, converting hours to minutes by multiplying by

60

gives exactly

15

minutes.

Adım Adım Çözüm

1

Calculate the time required in hours.

0.25

hours

Time is equal to distance divided by rate. Dividing

10

miles by

40

miles per hour gives

0.25

hours.

2

Convert the time from hours into minutes.

15

minutes

Since there are

60

minutes in an hour, multiplying

0.25

hours by

60

yields

15

minutes.

Anahtar Kavram

Calculating elapsed time using the distance formula and converting units of time.

Soru 28Soru →

During a training exercise, a reconnaissance team travels a distance of $18$ miles in exactly $45$ minutes using all-terrain vehicles. What is their average speed in miles per hour?

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

24

To find the average speed in miles per hour, the travel time must first be converted into hours. Since there are

60

minutes in an hour,

45

minutes is equal to

0.75

hours (or

\frac{3}{4}

of an hour). Dividing the distance of

18

miles by the time of

0.75

hours yields a rate of

24

miles per hour.

Adım Adım Çözüm

1

Convert the travel time from minutes to hours.

45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}

(or

\frac{3}{4}

hour).

The speed is requested in miles per hour, so the time must be converted to hours to match the units of the rate.

2

Calculate the average speed using the rate formula

r = \frac{d}{t}

.

r = \frac{18 \text{ miles}}{0.75 \text{ hours}} = 24 \text{ mph}

.

Rate equals total distance divided by total time.

Anahtar Kavram

Calculating rate with necessary time unit conversions

Tahmini Süre:1m 0s

Soru 29Soru →

A military transport helicopter flies a distance of $120$ miles between two bases. If the flight takes exactly $40$ minutes, what is the helicopter's average speed in miles per hour?

300

80

180

3

Cevabı ve açıklamayı göster

Cevap: $180$

Cevap

The helicopter's average speed is

180

miles per hour.

To find the correct speed in miles per hour, the travel time must first be converted to hours. Since

40

minutes is

\frac{40}{60}

or

\frac{2}{3}

of an hour, dividing the distance of

120

miles by

\frac{2}{3}

of an hour yields

180

miles per hour.

Adım Adım Çözüm

1

Convert the travel time from minutes to hours.

40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}

.

The requested rate is in miles per hour, so the time unit must be converted to hours before calculating.

2

Set up the rate formula using the distance and the converted time.

r = \frac{120 \text{ miles}}{\frac{2}{3} \text{ hours}}

.

The formula for finding average speed is rate equals distance divided by time (

r = \frac{d}{t}

).

3

Solve for the rate by dividing the whole number by the fraction.

120 \div \frac{2}{3} = 120 \times \frac{3}{2} = \frac{360}{2} = 180 \text{ mph}

.

Dividing by a fraction is achieved by multiplying by its reciprocal.

Anahtar Kavram

Average speed is calculated by dividing total distance by total time (

r = \frac{d}{t}

). When the required rate uses different units than the provided information, a unit conversion must be performed first.

Soru 30Soru →

A military fighter jet flies a mission in two segments. It travels the first $1000$ miles in $1$ hour. Then, it travels an additional $200$ miles in $15$ minutes to reach its destination. What is the average speed of the jet for the entire mission, in miles per hour?

16

75

900

960

Cevabı ve açıklamayı göster

Cevap: 960

Cevap

960

The correct average speed is found by dividing the total distance traveled (

1200

miles) by the total flight time in hours (

1.25

hours). Dividing

1200

by

1.25

yields

960

miles per hour.

Adım Adım Çözüm

1

Calculate the total distance traveled.

1000 \text{ miles} + 200 \text{ miles} = 1200 \text{ miles}

To find average speed for an entire trip, you first need the total distance covered.

2

Convert the total time into a single, consistent unit (hours).

1 \text{ hour} + 15 \text{ minutes} = 1 \text{ hour} + 0.25 \text{ hours} = 1.25 \text{ hours}

Since the question asks for miles per hour, the time must be expressed entirely in hours before dividing.

3

Calculate the average speed using the total distance and total time.

1200 \div 1.25 = 960 \text{ mph}

The formula for average speed is Total Distance divided by Total Time.

Anahtar Kavram

Average speed is calculated by dividing the total distance traveled by the total time taken. It is not the simple arithmetic mean of different speeds.

Tahmini Süre:1m 0s

Soru 31Soru →

A naval supply ship travels $150$ nautical miles in $10$ hours, and then travels an additional $90$ nautical miles in $5$ hours. What is the ship's average speed for the entire trip, in knots (nautical miles per hour)?

Cevabı ve açıklamayı göster

Cevap: 16

Cevap

16 knots

The overall average speed is calculated correctly by finding the total distance (

150 + 90 = 240

nautical miles) and dividing it by the total time (

10 + 5 = 15

hours). This calculation (

240 \div 15

) results in exactly

16

knots.

Adım Adım Çözüm

1

Calculate the total distance traveled for the entire trip.

150 + 90 = 240

nautical miles

Finding average speed requires knowing the complete distance covered across all segments of the trip.

2

Calculate the total time taken for the entire trip.

10 + 5 = 15

hours

Finding average speed requires knowing the total elapsed time.

3

Divide the total distance by the total time.

240 \div 15 = 16

knots

The formula for average speed is Total Distance divided by Total Time.

Anahtar Kavram

Average speed is calculated by dividing the total distance traveled by the total time taken.

Soru 32Soru →

A logistics battalion is coordinating different transport missions. Match each vehicle's specific mission profile with its correct calculated travel time, average speed, or arrival time.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The logistics mission profiles match successfully by applying the distance formula and executing necessary time conversions (e.g.,

2.25

hours is

2

hours and

15

minutes, and

30

minutes is

0.5

hours).

Each match strictly follows the distance formula

d = r \times t

, correctly manipulating the variables and converting fractional hours to minutes or minutes to hours where required.

Adım Adım Çözüm

1

Calculate the travel time for the supply truck.

Total travel time of

2

hours and

15

minutes

Applying

t = d \div r

(

90 \div 40 = 2.25

hours) and converting the decimal remainder to minutes (

0.25 \times 60 = 15

).

2

Calculate the average speed of the patrol boat.

Average speed of

30

mph

Applying

r = d \div t

(

135 \div 4.5 = 30

).

3

Calculate the arrival time of the armored transport.

Arrival time of 1100 hours

Applying

t = d \div r

(

165 \div 55 = 3

hours), then adding

3

hours to 0800 hours.

4

Calculate the average speed of the medevac helicopter.

Average speed of

150

mph

Converting

30

minutes to

0.5

hours, then applying

r = d \div t

(

75 \div 0.5 = 150

).

Anahtar Kavram

Applying the fundamental distance relationship (

d = r \times t

) to calculate unknown rates and times, while managing unit conversions and clock mathematics.

Tahmini Süre:2m 0s

Soru 33Soru →

An engineering platoon is paving a temporary runway. If their paving machine operates at a constant rate of $20$ feet per minute, how many hours will it take to pave a continuous $3,000$ -foot section?

2.3

2.5

25

150

Cevabı ve açıklamayı göster

Cevap: $2.5$

Cevap

The paving process will take 2.5 hours.

The correct answer is found by taking the total distance (

3,000

feet) and dividing it by the rate (

20

feet per minute) to get a total time of

150

minutes. Since there are

60

minutes in an hour, dividing

150

by

60

yields exactly

2.5

hours.

Adım Adım Çözüm

1

Determine the required time in the given units (minutes).

Time =

3,000 \div 20 = 150

minutes.

Using the formula Time = Distance ÷ Rate finds the duration in the same unit of time used by the rate.

2

Convert the calculated time from minutes to hours.

150 \div 60 = 2.5

hours.

The question explicitly asks for the final answer in hours, so the time in minutes must be divided by 60.

Anahtar Kavram

Calculating elapsed time using the distance formula (

t = d/r

) and performing time unit conversions.

Tahmini Süre:1m 30s

Soru 34Soru →

A delivery truck travels $40$ miles during the first $1$ hour of its route. It then travels another $75$ miles in $1$ hour and $30$ minutes. What is the truck's overall average speed for the entire trip?

45 mph

46 mph

50 mph

115 mph

Cevabı ve açıklamayı göster

Cevap: 46 mph

Cevap

46 mph

To find the overall average speed, divide the total distance by the total time. The total distance is

40 + 75 = 115

miles. The total time is

1

hour plus

1

hour and

30

minutes. Since

30

minutes is

0.5

hours, the total time is

1 + 1.5 = 2.5

hours. Dividing

115

miles by

2.5

hours gives an average speed of

46

mph.

Adım Adım Çözüm

1

Calculate the total distance traveled.

Total distance =

40 + 75 = 115

miles.

Average speed requires knowing the total distance of the trip.

2

Calculate the total time in consistent units (hours).

Total time =

1

hour +

1.5

hours =

2.5

hours.

Average speed requires the total time. The

30

minutes must be converted to

0.5

hours to match the unit.

3

Divide the total distance by the total time to find the average speed.

115 \div 2.5 = 46

mph.

The standard formula for average speed is total distance divided by total time.

Anahtar Kavram

Average speed is found by dividing the total distance of a journey by the total time it took to complete it.

Tahmini Süre:1m 0s

Soru 35Soru →

A supply convoy is scheduled to travel a total distance of $135$ miles to a forward operating base in exactly $3$ hours and $30$ minutes. For the first $90$ minutes, the convoy travels along a secured highway at an average rate of $50$ miles per hour. For the remainder of the route, what must be the convoy's average rate of speed, in miles per hour, to arrive exactly on time?

Cevabı ve açıklamayı göster

Cevap: 30

Cevap

30

The convoy must cover the remaining

60

miles in the remaining

2.0

hours, which requires an average speed of

30

miles per hour.

Adım Adım Çözüm

1

Convert the given travel times from minutes to hours.

3

hours and

30

minutes =

3.5

hours.

90

minutes =

1.5

hours.

Since the speed is given in miles per hour, all time values must be in hours.

2

Calculate the distance covered on the secured highway.

50 \text{ miles/hour} \times 1.5 \text{ hours} = 75 \text{ miles}

To find out how much of the total distance has already been traveled.

3

Calculate the remaining distance to the forward operating base.

135 \text{ miles} - 75 \text{ miles} = 60 \text{ miles}

This is the distance that must be covered during the off-road portion of the route.

4

Calculate the remaining travel time available.

3.5 \text{ hours} - 1.5 \text{ hours} = 2.0 \text{ hours}

This is the time limit for completing the rest of the journey.

5

Calculate the required average speed for the remaining distance.

60 \text{ miles} \div 2.0 \text{ hours} = 30 \text{ miles per hour}

Rate equals distance divided by time (

r = \frac{d}{t}

).

Anahtar Kavram

Calculating Rate and Time

Alternatif Yöntem

You could set up an algebraic equation for the total distance:

(50 \times 1.5) + (r \times 2.0) = 135

. Solving for

r

:

75 + 2r = 135

, so

2r = 60

, which means

r = 30

.

Tahmini Süre:1m 30s

Soru 36Soru →

A passenger train travels $80$ miles in $2$ hours. It then switches to a regional track and travels an additional $30$ miles in $3$ hours. Calculate the train's overall average speed for the entire journey.

Aşağıdaki boşlukları doldurun

The train's overall average speed is miles per hour.

Cevabı ve açıklamayı göster

Cevap

22

To calculate the average speed for the entire journey, determine the total distance traveled (

80 + 30 = 110

miles) and the total time taken (

2 + 3 = 5

hours). Dividing the total distance by the total time (

110 \div 5

) gives an average speed of

22

miles per hour.

Adım Adım Çözüm

1

Calculate the total distance traveled.

80 + 30 = 110 miles

Average speed requires the total distance for all segments of the trip combined.

2

Calculate the total time taken.

2 + 3 = 5 hours

Average speed requires the total time duration for all segments.

3

Divide the total distance by the total time.

110 / 5 = 22

The formula for overall average speed is Total Distance divided by Total Time.

Anahtar Kavram

Average speed is found by dividing the total distance by the total time, not by averaging the individual speeds of different segments.

Soru 37Soru →

A submarine needs to travel a distance of $45$ nautical miles to reach a designated patrol zone. If the submarine maintains a constant submerged speed of $18$ knots (nautical miles per hour), how many minutes will it take to reach the zone?

150

2.5

24

250

Cevabı ve açıklamayı göster

Cevap: $150$

Cevap

The submarine will take

150

minutes to reach the patrol zone.

The correct answer is found by dividing the total distance (

45

nautical miles) by the rate (

18

knots) to determine the time in hours (

2.5

hours). Then, this value is multiplied by

60

to convert hours into minutes, resulting in

150

minutes.

Adım Adım Çözüm

1

Calculate the time required in hours using the formula

\text{Time} = \text{Distance} / \text{Rate}

.

45 / 18 = 2.5

hours.

The distance is given in nautical miles and the rate is given in nautical miles per hour, so dividing them yields the time in hours.

2

Convert the time from hours into minutes.

2.5 \times 60 = 150

minutes.

The question specifically asks for the travel time in minutes. There are

60

minutes in

1

hour.

Anahtar Kavram

Calculating time from rate and distance, followed by unit conversion.

Soru 38Soru →

Determine the unknown rate or time for each of the following military travel profiles by matching them to their correctly calculated values.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The supply truck travels at

52

mph, the aircraft takes

4

hours, the infantry squad marches at

3

mph, and the destroyer takes

4.5

hours.

Each match is correct because the standard distance relationships (

r = d/t

or

t = d/r

) are applied after standardizing all units. Knots are correctly identified as speed, and minutes are accurately converted into fractions of an hour.

Adım Adım Çözüm

1

Identify the given variables and the missing variable for each travel profile.

Two scenarios give distance and time (requiring rate), while two give distance and rate (requiring time).

This determines whether to use the formula

r = d/t

or

t = d/r

.

2

Convert mixed time units into a single fractional or decimal unit of hours.

2

hours

30

minutes becomes

2.5

hours.

2

hours

40

minutes becomes

2 \frac{2}{3}

or

8/3

hours.

Rates expressed in mph require time to be represented entirely in hours before dividing.

3

Calculate the missing values using the appropriate distance formula.

Truck:

130 \div 2.5 = 52

. Aircraft:

1,200 \div 300 = 4

. Squad:

8 \div (8/3) = 3

. Destroyer:

135 \div 30 = 4.5

.

Applying the correct operational relationship yields the final matched answers.

Anahtar Kavram

Calculating Rate and Time with Unit Conversions

Soru 39Soru →

A rescue helicopter flies $150$ miles to an offshore oil rig in $90$ minutes. The return flight to the base along the same route takes $150$ minutes due to strong headwinds. What is the helicopter's average speed in miles per hour for the entire round trip?

75

80

125

37.5

Cevabı ve açıklamayı göster

Cevap: 75

Cevap

75

The average speed for an entire trip is found by dividing the total round-trip distance (

300

miles) by the total round-trip time in hours (

4

hours), which gives

75

miles per hour.

Adım Adım Çözüm

1

Calculate the total distance traveled for the round trip.

150 \text{ miles} + 150 \text{ miles} = 300 \text{ miles}

Average speed is based on the entire distance covered during the trip.

2

Convert the flight times from minutes to hours.

90 \text{ minutes} = 1.5 \text{ hours}

, and

150 \text{ minutes} = 2.5 \text{ hours}

The question asks for the speed in miles per hour, so the time units must be converted to hours.

3

Calculate the total time elapsed for the round trip.

1.5 \text{ hours} + 2.5 \text{ hours} = 4 \text{ hours}

Average speed is based on the total time taken for the entire journey.

4

Divide the total distance by the total time.

300 \div 4 = 75 \text{ mph}

The formula for average speed is Total Distance divided by Total Time.

Anahtar Kavram

Average Speed

Soru 40Soru →

Two cyclists, Sarah and Mike, start at opposite ends of a $60$ -mile trail and ride directly toward each other. Sarah rides at a constant speed of $12$ mph, and Mike rides at a constant speed of $18$ mph. How many hours will it take for them to meet?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

2

Because the cyclists are moving directly toward each other, their gap closes at a combined rate of

30

mph (

12

mph +

18

mph). Dividing the total initial distance of

60

miles by this combined rate yields exactly

2

hours.

Adım Adım Çözüm

1

Calculate the combined relative speed.

30 mph

When objects move toward each other from opposite directions, their relative speed is the sum of their individual speeds (

12 + 18 = 30

).

2

Calculate the time required to meet.

2 hours

Using the formula Time = Distance / Rate, divide the total distance (

60

miles) by the relative speed (

30

mph).

Anahtar Kavram

Relative Motion and Catch-Up Scenarios

Time, Rate, and Distance

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