Calculating Rate and Time Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Match each military travel scenario with its calculated average speed or travel time.

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Cevabı ve açıklamayı göster

Cevap

The matches are: convoy speed is 45 mph, patrol boat time is 30 minutes, helicopter speed is 160 mph, and humvee time is 120 minutes.

Each scenario requires applying the fundamental relationship between distance, rate, and time (

d = rt

). For scenarios asking for minutes, the calculated hours are multiplied by 60. For scenarios given in minutes but requiring mph, the minutes are divided by 60.

Adım Adım Çözüm

1

Calculate the speed for the convoy.

180 \text{ miles} \div 4 \text{ hours} = 45 \text{ mph}

Average speed is found by dividing total distance by total time.

2

Calculate the travel time for the patrol boat.

15 \text{ miles} \div 30 \text{ mph} = 0.5 \text{ hours}

.

0.5 \times 60 = 30 \text{ minutes}

.

Time is distance divided by rate. The result in hours must be multiplied by 60 to find minutes.

3

Calculate the speed for the helicopter.

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

.

240 \text{ miles} \div 1.5 \text{ hours} = 160 \text{ mph}

.

Speed in mph requires the time to be in hours, so minutes are divided by 60 first.

4

Calculate the travel time for the humvee.

110 \text{ miles} \div 55 \text{ mph} = 2 \text{ hours}

.

2 \times 60 = 120 \text{ minutes}

.

Divide distance by rate to get hours, then multiply by 60 for minutes.

Anahtar Kavram

Calculating Rate and Time with Unit Conversions

Tahmini Süre:1m 30s

Soru 2Soru →

A squad of soldiers is conducting a foot march along a trail that is $12$ miles long. If they maintain a steady pace of $3$ miles per hour, how many hours will it take them to complete the march?

Cevabı ve açıklamayı göster

Cevap: 4

Cevap

4

Using the fundamental relationship

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

, we divide the total distance of

12

miles by the steady pace of

3

miles per hour. This calculation (

12 \div 3

) results in exactly

4

hours.

Adım Adım Çözüm

1

Identify the given values for the distance and the rate of travel.

Distance =

12

miles, Rate =

3

miles per hour.

These values are required to calculate the total elapsed time.

2

Apply the appropriate formula to find the time.

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

Time is equal to total distance divided by the speed.

3

Substitute the values and calculate the result.

\frac{12}{3} = 4

Dividing the distance by the rate gives the total time in hours.

Anahtar Kavram

Calculating elapsed time given distance and rate.

Tahmini Süre:45s

Soru 3Soru →

A naval submarine travels a total distance of $144$ miles in $4$ hours and $30$ minutes. Assuming a constant rate of travel, which of the following is the average speed of the submarine in miles per hour?

3.2

32

36

648

Cevabı ve açıklamayı göster

Cevap: $32$

Cevap

The average speed is

32

miles per hour.

To find the average speed, the total distance must be divided by the total time in hours. First, convert

4

hours and

30

minutes to

4.5

hours. Then, dividing

144

miles by

4.5

hours gives an average speed of

32

miles per hour.

Adım Adım Çözüm

1

Convert the total travel time into a single unit of hours.

4

hours and

30

minutes equals

4.5

hours.

Since the requested speed is in miles per hour, the time must be expressed purely in hours before calculating.

2

Apply the formula for average speed:

Speed = Distance \div Time

.

Speed = 144 \div 4.5

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

3

Perform the division.

1440 \div 45 = 32

Shifting the decimal point one place to the right for both the dividend and divisor makes the calculation easier, resulting in

32

miles per hour.

Anahtar Kavram

Calculating Rate given Distance and Time

Soru 4Soru →

Match each travel scenario to the correct amount of time it takes to complete the journey.

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Cevabı ve açıklamayı göster

Cevap

The delivery van takes 3 hours, the cargo ship takes 4 hours, the marathon runner takes 2 hours, and the commuter train takes 5 hours.

Each correct match is determined by taking the stated distance in miles and dividing it by the average speed in miles per hour (

t = \frac{d}{r}

). Because the difficulty is intentionally basic, all divisions result in clean, whole-number integer hours.

Adım Adım Çözüm

1

Identify the given distance (

d

) and rate (

r

) for each scenario.

Van: (

150

mi,

50

mph), Ship: (

80

mi,

20

mph), Runner: (

16

mi,

8

mph), Train: (

300

mi,

60

mph).

These variables are required to apply the fundamental distance formula.

2

Apply the formula for calculating time:

t = \frac{d}{r}

.

Van:

\frac{150}{50} = 3

. Ship:

\frac{80}{20} = 4

. Runner:

\frac{16}{8} = 2

. Train:

\frac{300}{60} = 5

.

Dividing the total distance traveled by the constant rate yields the total elapsed time.

Anahtar Kavram

Calculating elapsed time using the distance-rate-time relationship (

t = \frac{d}{r}

).

Soru 5Soru →

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 6Soru →

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 7Soru →

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 8Soru →

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 9Soru →

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 10Soru →

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.

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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 11Soru →

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 12Soru →

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 13Soru →

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 14Soru →

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

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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 15Soru →

A riverine patrol boat is tasked with delivering supplies to a forward operating base. The boat needs to cover a distance of $3.5$ miles upstream. If it maintains a constant speed over ground of $14$ miles per hour and departs at $0945$ hours, at what time will the boat arrive at its destination?

1215

hours

1000

hours

1345

hours

1010

hours

Cevabı ve açıklamayı göster

Cevap: $1000$ hours

Cevap

The boat will arrive at

1000

hours.

To find the arrival time, first calculate the travel time. Using the formula Time = Distance / Rate, the time is

3.5 / 14 = 0.25

hours. Next, convert

0.25

hours to minutes by multiplying by

60

, which equals

15

minutes. Finally, add the

15

minutes of travel time to the departure time of

0945

hours. Adding

15

minutes to

0945

brings the clock time exactly to

1000

hours.

Adım Adım Çözüm

1

Calculate the travel time in hours by dividing the distance by the rate.

t = \frac{3.5 \text{ miles}}{14 \text{ mph}} = 0.25 \text{ hours}

The formula for time is Time = Distance / Rate.

2

Convert the calculated time from hours to minutes.

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

Clock time additions are easier and more accurate when working with minutes rather than fractional hours.

3

Add the travel time in minutes to the departure time to find the arrival time.

0945 \text{ hours} + 15 \text{ minutes} = 1000 \text{ hours}

The arrival time is the departure time plus the elapsed travel time. Adding 15 minutes to 45 minutes completes the 60-minute hour, rolling the time over to 1000.

Anahtar Kavram

Calculating elapsed time using the distance formula (

t = d/r

) and converting fractional hours to minutes to determine clock arrival time.

Soru 16Soru →

An armored vehicle traverses an $18$ -mile desert route. It travels the first $10$ miles at a constant speed of $20$ miles per hour. If the vehicle completes the entire route in exactly $45$ minutes, what is its speed in miles per hour for the remaining distance?

Cevabı ve açıklamayı göster

Cevap: 32

Cevap

The speed for the remaining distance is

32

miles per hour.

To find the unknown speed, you must isolate the distance and time for the final segment. First, the time for the

10

-mile stretch is calculated as

0.5

hours, which is equivalent to

30

minutes. Subtracting this from the total

45

minutes leaves

15

minutes (or

0.25

hours) to travel the remaining

8

miles. Dividing the

8

miles by the

0.25

hours of remaining time yields a final speed of

32

miles per hour.

Adım Adım Çözüm

1

Calculate the time for the first segment.

10 \text{ miles} \div 20 \text{ mph} = 0.5 \text{ hours}

You need to know how much time was spent on the first segment to determine the time left for the remainder of the route.

2

Convert the first segment's time into minutes.

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

The total time is provided in minutes (

45

minutes), so making the units consistent allows you to easily subtract and find the remaining time.

3

Find the remaining time available.

45 \text{ minutes} - 30 \text{ minutes} = 15 \text{ minutes}

This step determines exactly how much time the vehicle has to complete the rest of the route.

4

Convert the remaining time into hours.

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

Since the requested final speed must be in miles per hour, the time value needs to be expressed in hours.

5

Determine the remaining distance.

18 \text{ miles} - 10 \text{ miles} = 8 \text{ miles}

This is the physical distance the vehicle must cover during the final

15

minutes.

6

Calculate the speed for the final segment.

8 \text{ miles} \div 0.25 \text{ hours} = 32 \text{ mph}

Dividing the remaining distance by the remaining time gives the required speed.

Anahtar Kavram

Calculating unknown rates in multi-part trips by finding intermediate distances and times, and converting units correctly.

Soru 17Soru →

A logistics drone is deployed to deliver medical supplies to a remote outpost $105$ miles away. The drone travels at a constant speed of $42$ miles per hour. If the drone departs the base at $0745$ hours, at what time will it arrive at the outpost?

1015

hours

1035

hours

0809

hours

0800

hours

Cevabı ve açıklamayı göster

Cevap: $1015$ hours

Cevap

The correct arrival time is

1015

hours.

The drone travels

105

miles at

42

miles per hour, which takes

2.5

hours (or

2

hours and

30

minutes). Adding

2

hours and

30

minutes to the departure time of

0745

hours results in a final arrival time of

1015

hours.

Adım Adım Çözüm

1

Calculate the total travel time in hours.

Time = 105 \text{ miles} / 42 \text{ mph} = 2.5 \text{ hours}

.

The formula for finding time is

Time = Distance / Rate

.

2

Convert the decimal portion of the time into minutes.

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

. The total travel time is

2

hours and

30

minutes.

Clock time requires hours and minutes, not decimal fractions of an hour.

3

Add the travel time to the departure time to find the arrival time.

0745 \text{ hours} + 2 \text{ hours and } 30 \text{ minutes} = 1015 \text{ hours}

.

Adding

2

hours to

0745

gives

0945

. Adding

30

minutes to

0945

advances the clock past the hour (

60

minutes) to

1015

.

Anahtar Kavram

Calculating elapsed time using the distance formula (

t = d/r

) and converting decimal hours to standard clock time.

Soru 18Soru →

A transport aircraft is flying a $1,200$ -nautical-mile resupply mission. It flies the first $600$ nautical miles at a cruising speed of $300$ knots. Due to headwind conditions, it flies the remaining $600$ nautical miles at a reduced speed of $240$ knots. What is the total flight time for this mission?

4 hours 30 minutes

4 hours 50 minutes

4 hours 27 minutes

2 hours 30 minutes

Cevabı ve açıklamayı göster

Cevap: 4 hours 30 minutes

Cevap

4 hours 30 minutes

The correct answer accurately finds the time for each leg of the journey by dividing distance by speed. The first leg takes 2 hours (

600 \div 300

) and the second leg takes 2.5 hours (

600 \div 240

). Combining these yields 4.5 hours, which is equal to 4 hours and 30 minutes.

Adım Adım Çözüm

1

Calculate the time taken for the first half of the mission.

600 \div 300 = 2

hours.

Time is calculated by dividing the distance by the rate for that specific segment.

2

Calculate the time taken for the second half of the mission.

600 \div 240 = 2.5

hours.

The rate changed, so this segment's time must be calculated independently using its specific distance and rate.

3

Add the times of both segments to find the total flight time in hours.

2 + 2.5 = 4.5

hours.

The total duration of the mission is the sum of the time spent on all individual segments.

4

Convert the fractional hour into minutes.

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

minutes. Total time is 4 hours and 30 minutes.

Standard time format requires separating whole hours and converting the remaining fraction into minutes.

Anahtar Kavram

Calculating Rate and Time for Multi-leg Journeys

Tahmini Süre:1m 15s

Soru 19Soru →

A military convoy must complete a 180-mile route to a forward operating base in exactly 4 hours. The convoy travels at an average speed of 50 mph for 90 minutes, then halts for a 60-minute security checkpoint. What average speed, in mph, must the convoy maintain for the remainder of the journey to arrive exactly on time?

42

45

54

70

Cevabı ve açıklamayı göster

Cevap: 70

Cevap

70

The convoy has already traveled 75 miles in 1.5 hours, and stopped for 1.0 hour. This means 2.5 hours have elapsed in total, leaving 1.5 hours to travel the remaining 105 miles. Dividing 105 miles by 1.5 hours results in a required speed of 70 mph.

Adım Adım Çözüm

1

Convert the travel and checkpoint times from minutes to hours.

90 minutes = 1.5 hours; 60 minutes = 1.0 hour.

Speed is given in miles per hour (mph), so time must be uniformly expressed in hours.

2

Calculate the distance covered during the first leg of the journey.

50 mph × 1.5 hours = 75 miles.

This establishes how much of the 180-mile route has already been completed before the stop.

3

Determine the remaining distance to the base.

180 miles - 75 miles = 105 miles.

This is the distance that must be covered in the final driving leg.

4

Calculate the time remaining to complete the route.

4 hours - (1.5 hours + 1.0 hour) = 4 - 2.5 = 1.5 hours.

The convoy must arrive exactly 4 hours after initial departure, accounting for both active driving and stopped time.

5

Calculate the required average speed for the final leg.

105 miles ÷ 1.5 hours = 70 mph.

Rate equals distance divided by time.

Anahtar Kavram

Calculating Rate and Time

Tahmini Süre:2m 30s

Soru 20Soru →

A rescue helicopter departs base at $0915$ hours for a distress signal $120$ miles away. It flies outbound at $160$ mph, spends $30$ minutes on scene, and returns along the same route at $120$ mph. At what time does the helicopter arrive back at the base?

1130 hours

1030 hours

1200 hours

1205 hours

Cevabı ve açıklamayı göster

Cevap: 1130 hours

Cevap

1130 hours

The correct arrival time is found by determining the time for each flight leg individually (Distance / Rate), ensuring decimal hours are correctly converted into minutes, adding the on-scene time, and then adding that total elapsed duration to the initial departure time.

Adım Adım Çözüm

1

Calculate the duration of the outbound flight.

0.75

hours (or

45

minutes)

Using the formula

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

, the outbound flight takes

\frac{120}{160} = 0.75

hours. To convert to minutes, multiply by

60

:

0.75 \times 60 = 45

minutes.

2

Calculate the duration of the return flight.

1

hour (or

60

minutes)

The helicopter returns along the same

120

-mile route at a speed of

120

mph.

\frac{120}{120} = 1

hour.

3

Calculate the total mission duration.

135

minutes (or

2

hours

15

minutes)

Sum the three segments of the mission: Outbound (

45

minutes) + On-scene (

30

minutes) + Return (

60

minutes) =

135

minutes total.

4

Determine the final arrival time based on the departure time.

1130

hours

Add the total duration of

2

hours and

15

minutes to the departure time of

0915

hours.

0915 + 2\text{ hours } 15\text{ minutes} = 1130

hours.

Anahtar Kavram

Calculating elapsed time using the relationship between distance and rate, converting decimal hours to minutes, and correctly summing components of a multi-leg journey.

Calculating Rate and Time

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