Time, Rate, and Distance Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 3

Soru 41Soru →

Two cars leave a parking lot at the same time and travel in opposite directions on a straight highway. One car travels at a constant speed of $40$ mph, and the other car travels at a constant speed of $50$ mph. How many hours will it take for the two cars to be exactly $270$ miles apart?

3

6

27

30

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

It will take 3 hours for the cars to be 270 miles apart.

The correct answer is 3. Since the cars are traveling in opposite directions, their speeds are added to find the total rate at which they are separating:

40 \text{ mph} + 50 \text{ mph} = 90 \text{ mph}

. To find the time it takes to separate by

270

miles, divide the total distance by the combined relative speed:

270 \div 90 = 3

hours.

Adım Adım Çözüm

1

Determine the relative speed of the two cars.

40 + 50 = 90

mph

When two objects move in opposite directions away from each other, their relative speed is the sum of their individual speeds.

2

Calculate the time required to reach the target distance.

270 \div 90 = 3

hours

Time equals total distance divided by the relative speed (

T = D \div R

).

Anahtar Kavram

Relative Motion (Opposite Directions)

Soru 42Soru →

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 43Soru →

Two inspection drones take off from the same cellular tower at the same time and fly in opposite directions along a straight power line. Drone A flies at $15$ mph and Drone B flies at $25$ mph. How many miles apart are the two drones after $2$ hours?

Cevabı ve açıklamayı göster

Cevap: 80; 80 miles; 80 mi; eighty

Cevap

The drones are 80 miles apart.

Since the drones travel in opposite directions, their relative speed is the sum of their individual speeds (

15 + 25 = 40

mph). Over the course of

2

hours, the distance between them becomes

40 \times 2 = 80

miles.

Adım Adım Çözüm

1

Calculate the combined relative speed of both drones.

15 + 25 = 40

mph

Because the drones are flying in opposite directions, the distance between them increases at a rate equal to the sum of their individual speeds.

2

Multiply the relative speed by the time traveled.

40 \times 2 = 80

miles

Total distance is found by multiplying the relative speed by the total time (

D = r \times t

).

Anahtar Kavram

Calculating separation distance for objects moving in opposite directions using relative speed.

Tahmini Süre:45s

Soru 44Soru →

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 45Soru →

Two motorboats leave a marina at the same time, traveling in opposite directions on a straight path. One boat travels at a constant speed of $18$ mph, and the other travels at a constant speed of $22$ mph. How many minutes will it take for the two boats to be exactly $120$ miles apart?

3

180

360

1800

Cevabı ve açıklamayı göster

Cevap: 180

Cevap

180

Because the boats are moving in opposite directions, their relative speed of separation is the sum of their individual speeds: 18 mph + 22 mph = 40 mph. To find how long it takes to separate by 120 miles, divide the distance by the relative rate: 120 / 40 = 3 hours. Finally, convert 3 hours into minutes by multiplying by 60, resulting in 180 minutes.

Adım Adım Çözüm

1

Calculate the combined relative speed of the two boats.

18 + 22 = 40

mph

Because the boats are traveling in opposite directions, their speeds add together to create the rate at which they are separating.

2

Calculate the time in hours it takes to reach the target distance.

120 \div 40 = 3

hours

Using the formula Time = Distance / Rate, dividing the total distance by the relative speed gives the time in hours.

3

Convert the time from hours to minutes.

3 \times 60 = 180

minutes

The question explicitly asks for the final answer in minutes, not hours.

Anahtar Kavram

Relative Motion and Catch-Up Scenarios

Soru 46Soru →

A cyclist is riding on a paved trail at a constant speed of $15 \text{ miles per hour}$ . At this rate, how many miles will the cyclist travel in $40 \text{ minutes}$ ?

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10

The distance is found by matching the time units to the speed units. First, convert

40 \text{ minutes}

into

\frac{2}{3} \text{ hours}

. Then, multiply the speed (

15 \text{ mph}

) by the time (

\frac{2}{3} \text{ hours}

) to get exactly 10 miles.

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 speed is given in miles per hour, so the time must be converted to hours before using it in the distance formula.

2

Calculate the total distance traveled.

15 \times \frac{2}{3} = 10 \text{ miles}

Distance is equal to the rate (speed) multiplied by the time (

d = r \times t

).

Anahtar Kavram

Unit conversions for time in rate problems

Soru 47Soru →

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 48Soru →

A military patrol boat consumes 40 gallons of fuel per hour and travels at a constant speed of 20 miles per hour. If the boat completes a round trip to an island 60 miles away, how many gallons of fuel will it use in total?

6

60

120

240

Cevabı ve açıklamayı göster

Cevap: 240

Cevap

The boat will use a total of 240 gallons of fuel.

First, find the total distance for the round trip, which is

120

miles (

60

miles each way). At a speed of

20

miles per hour, the entire trip takes

6

hours (

120 \div 20

). Since the boat burns

40

gallons per hour, multiply the time by the fuel rate to find the total fuel consumed:

6 \times 40 = 240

gallons.

Adım Adım Çözüm

1

Calculate the total distance for the round trip.

60 \times 2 = 120

miles

The boat must travel to the island and then return along the same route.

2

Calculate the total travel time in hours.

120 \div 20 = 6

hours

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

3

Calculate the total fuel consumed.

6 \times 40 = 240

gallons

Total fuel used is the travel time multiplied by the hourly fuel consumption rate.

Anahtar Kavram

Calculating total fuel consumption for a round trip using speed, distance, and fuel rate.

Alternatif Yöntem

Find the fuel consumption per mile first:

40

gallons per hour

\div 20

miles per hour =

2

gallons per mile. Then, multiply this rate by the total round-trip distance:

120

miles

\times 2

gallons per mile =

240

gallons.

Tahmini Süre:45s

Soru 49Soru →

Match each vehicle trip scenario to the total number of gallons of fuel required to complete the journey.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The scout vehicle requires 5 gallons, the transport truck requires 12 gallons, the command SUV requires 16 gallons, and the hybrid commuter car requires 7 gallons.

The correct pairings are found by properly applying the formula: Gallons Consumed = Total Distance ÷ Fuel Efficiency (MPG). Performing this calculation for each scenario accurately identifies the fuel requirement.

Adım Adım Çözüm

1

Calculate the fuel required for the scout vehicle.

150 / 30 = 5 gallons.

Dividing the total travel distance by the vehicle's fuel efficiency (MPG) determines the total fuel consumed.

2

Calculate the fuel required for the transport truck.

240 / 20 = 12 gallons.

Dividing the total travel distance by the vehicle's fuel efficiency (MPG) determines the total fuel consumed.

3

Calculate the fuel required for the command SUV.

400 / 25 = 16 gallons.

Dividing the total travel distance by the vehicle's fuel efficiency (MPG) determines the total fuel consumed.

4

Calculate the fuel required for the hybrid commuter car.

350 / 50 = 7 gallons.

Dividing the total travel distance by the vehicle's fuel efficiency (MPG) determines the total fuel consumed.

Anahtar Kavram

Calculating total fuel consumption given total travel distance and fuel efficiency.

Soru 50Soru →

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 51Soru →

A courier's motorcycle has a fuel efficiency of $40$ miles per gallon. The courier uses exactly $2.5$ gallons of fuel to complete a round trip from the dispatch center to a customer's location and back. What is the one-way distance between the dispatch center and the customer's location?

5

16

50

100

Cevabı ve açıklamayı göster

Cevap: 50

Cevap

The one-way distance is

50

miles.

To find the one-way distance, first determine the total distance traveled by multiplying the fuel efficiency by the amount of fuel used:

40 \text{ miles/gallon} \times 2.5 \text{ gallons} = 100 \text{ miles}

. Since this is a round trip, divide the total distance by

2

to find the one-way distance:

100 \div 2 = 50 \text{ miles}

.

Adım Adım Çözüm

1

Calculate the total distance traveled using the fuel efficiency and total fuel used.

40 \text{ miles/gallon} \times 2.5 \text{ gallons} = 100 \text{ miles}

Total distance is the product of the rate of fuel consumption (efficiency) and the amount of fuel consumed.

2

Calculate the one-way distance by dividing the total round trip distance in half.

100 \text{ miles} \div 2 = 50 \text{ miles}

A round trip consists of two equal segments (going and returning), so the one-way distance is half of the total distance.

Anahtar Kavram

Calculating distance from fuel efficiency and separating round trip distance into one-way legs.

Soru 52Soru →

Fill in the blank with the correct numeric value.

Aşağıdaki boşlukları doldurun

A military dispatch rider travels

75

miles on a highway in

1

hour and

30

minutes. He then travels an additional

25

miles on secondary roads in

1

hour. The rider's average speed for the entire trip is miles per hour.

Cevabı ve açıklamayı göster

Cevap

The average speed for the entire trip is 40 miles per hour.

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

100

miles) by the total travel time (

2.5

hours), which results in exactly

40

miles per hour.

Adım Adım Çözüm

1

Calculate the total distance traveled.

75 + 25 = 100

miles.

Average speed calculation requires the total distance of the trip.

2

Convert all time measurements to hours and calculate the total time.

1

hour and

30

minutes is equivalent to

1.5

hours. Total time

= 1.5 + 1 = 2.5

hours.

The requested rate is in miles per hour, so the total time must be consistently represented in hours.

3

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

100 \div 2.5 = 40

miles per hour.

The fundamental formula for average speed is

\text{Total Distance} \div \text{Total Time}

.

Anahtar Kavram

Average speed is calculated by dividing the total distance traveled by the total time taken for the trip, not by taking the arithmetic mean of the individual segment speeds.

Soru 53Soru →

During a training exercise, an army jeep travels at a constant fuel consumption rate of 14 miles per gallon. If the jeep starts with exactly 8 gallons of fuel in its tank, what is the maximum number of miles the jeep can travel before running out of gas?

Cevabı ve açıklamayı göster

Cevap: 112

Cevap

112

The correct answer is found by multiplying the fuel efficiency rate (14 miles per gallon) by the amount of fuel in the tank (8 gallons). 14 * 8 equals 112 miles.

Adım Adım Çözüm

1

Identify the given values

Fuel efficiency = 14 miles per gallon, Fuel available = 8 gallons

These are the necessary components to calculate total distance.

2

Calculate the total distance

14 * 8 = 112 miles

Distance is the product of the rate of fuel consumption (miles per gallon) and the total amount of fuel (gallons).

Anahtar Kavram

Calculating maximum travel range based on fuel efficiency and fuel volume.

Soru 54Soru →

An engineer battalion is transporting heavy equipment in a convoy to a forward operating base $210$ miles away. To arrive on schedule, the convoy must maintain an overall average speed of $42$ mph for the entire journey.

During the first leg, the convoy travels $120$ miles in $2$ hours. They then halt for $30$ minutes to inspect the equipment.

What average speed must the convoy maintain for the remainder of the trip to achieve the target overall average speed?

24 mph

30 mph

36 mph

60 mph

Cevabı ve açıklamayı göster

Cevap: 36 mph

Cevap

The convoy must maintain an average speed of 36 mph for the remainder of the trip.

To achieve an overall average speed of

42

mph over

210

miles, the total journey must take exactly

5

hours. The convoy has already used

2.5

hours (

2

hours driving +

0.5

hours resting) and covered

120

miles. This leaves

90

miles to be covered in the remaining

2.5

hours. Dividing the remaining distance by the remaining time (

90 / 2.5

) gives the required speed of

36

mph.

Adım Adım Çözüm

1

Calculate the total time required for the entire journey.

Total Time =

210 \text{ miles} / 42 \text{ mph} = 5 \text{ hours}

.

To find the time available for the second leg, we first need to know the total time allowed for the mission.

2

Calculate the time spent on the first leg and the rest stop.

Time Spent =

2 \text{ hours} + 30 \text{ minutes} = 2.5 \text{ hours}

.

The rest stop must be included in the total elapsed time because the overall average speed accounts for the entire duration of the journey.

3

Determine the remaining distance and remaining time for the final leg.

Remaining Distance =

210 - 120 = 90 \text{ miles}

.
Remaining Time =

5 - 2.5 = 2.5 \text{ hours}

.

Subtracting the distance already covered and the time already spent gives the parameters for the final segment.

4

Calculate the required average speed for the final leg.

Speed =

90 \text{ miles} / 2.5 \text{ hours} = 36 \text{ mph}

.

Average speed is always calculated as total distance divided by total time for that specific segment.

Anahtar Kavram

To find a missing speed in a multi-leg journey, use the total distance and target average speed to find the total allowed time. Subtract the time and distance already used (including rest stops) to find the parameters for the remaining leg.

Alternatif Yöntem

You can work entirely in minutes to avoid decimals. Total time is

300

minutes. Time spent is

150

minutes. Time remaining is

150

minutes. Speed needed is

90 \text{ miles} / 150 \text{ minutes} = 0.6 \text{ miles per minute}

. Multiply by

60

to convert to

36

mph.

Tahmini Süre:1m 30s

Soru 55Soru →

An armored cavalry troop conducts a training movement. They travel $45$ miles over rough terrain at a speed of $15$ miles per hour. After a $90$ -minute halt for vehicle maintenance, they proceed $75$ miles along a highway at $50$ miles per hour. What is their overall average speed, in miles per hour, for the entire operation?

Cevabı ve açıklamayı göster

Cevap: 20

Cevap

The overall average speed is

20

miles per hour.

The correct answer is

20

because average speed is the ratio of total distance to total time. The total distance is

120

miles (

45 + 75

). The total time includes the travel times (

3

hours and

1.5

hours) plus the maintenance halt (

1.5

hours), which equals

6

hours. Dividing

120

miles by

6

hours gives an overall average speed of

20

miles per hour.

Adım Adım Çözüm

1

Calculate the time taken for the first travel segment.

\frac{45}{15} = 3

hours

Time is required to determine the total elapsed time of the operation.

2

Convert the maintenance halt time from minutes to hours.

90

minutes

= 1.5

hours

All time units must be consistent (hours) before they can be added together.

3

Calculate the time taken for the second travel segment.

\frac{75}{50} = 1.5

hours

This gives the travel time for the final leg of the route.

4

Calculate the total distance traveled.

45 + 75 = 120

miles

Total distance is the numerator in the average speed formula.

5

Calculate the total elapsed time for the entire operation.

3 + 1.5 + 1.5 = 6

hours

Total time is the denominator in the average speed formula, and it must include the maintenance halt.

6

Calculate the overall average speed.

\frac{120}{6} = 20

miles per hour

Average speed is defined as the total distance divided by the total time.

Anahtar Kavram

Average speed is calculated by dividing the total distance traveled by the total time elapsed, including any rest stops or delays.

Soru 56Soru →

A medical supply drone is programmed to complete a $120$ -mile delivery route with a required overall average speed of $40$ miles per hour. During the first segment, the drone flies $60$ miles at an average speed of $30$ miles per hour. It then lands for a $20$ -minute battery swap. At what average speed must the drone fly for the remainder of the route to achieve its required overall average speed?

50

mph

60

mph

90

mph

150

mph

Cevabı ve açıklamayı göster

Cevap: $90$ mph

Cevap

The drone must fly at

90

mph for the remainder of the route.

To solve for a missing speed when an overall average is required, you must first find the total time allowed. For a

120

-mile trip at

40

mph, the drone has exactly

3

hours. The first leg took

2

hours (

60

miles

\div

30

mph), and the battery swap took

20

minutes. This leaves only

40

minutes (which is

2/3

of an hour) to travel the remaining

60

miles. Dividing

60

miles by

2/3

hours yields a required speed of

90

mph.

Adım Adım Çözüm

1

Calculate the total time allowed for the entire trip.

T_{total} = 120 \text{ miles} \div 40 \text{ mph} = 3 \text{ hours}

.

Overall average speed equals total distance divided by total time.

2

Calculate the time spent flying the first segment.

T_1 = 60 \text{ miles} \div 30 \text{ mph} = 2 \text{ hours}

.

Time equals distance divided by speed.

3

Determine the total time used so far, including the battery swap.

2 \text{ hours} + 20 \text{ minutes} = 2 \text{ hours and } 20 \text{ minutes}

.

Rest stops and delays must be included in total transit time.

4

Calculate the remaining time available.

3 \text{ hours} - 2 \text{ hours } 20 \text{ minutes} = 40 \text{ minutes}

.

Subtract the time already used from the total time allowed.

5

Convert the remaining time into hours.

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

.

Speed is required in miles per hour, so time must be in hours.

6

Calculate the remaining distance.

120 \text{ miles} - 60 \text{ miles} = 60 \text{ miles}

.

Subtract the distance already covered from the total distance.

7

Calculate the required average speed for the final segment.

V_2 = 60 \text{ miles} \div \frac{2}{3} \text{ hours} = 60 \times \frac{3}{2} = 90 \text{ mph}

.

Speed equals remaining distance divided by remaining time.

Anahtar Kavram

Average speed over a multi-segment journey is defined solely as the total distance divided by the total time. All stops, breaks, and varying speeds must be accounted for by combining their respective times.

Soru 57Soru →

Calculate the required average speed to complete the mission as specified. Enter your numerical answer in the blank.

Aşağıdaki boşlukları doldurun

A surveillance aircraft is assigned a

420

-mile mission route. The aircraft completes the first

240

miles of the route in

3

hours. To achieve an overall average speed of

60

miles per hour for the entire mission, the aircraft must complete the remaining distance at an average speed of miles per hour.

Cevabı ve açıklamayı göster

Cevap

45

To find the required speed for the second leg, you must first determine the total time allowed for the trip. Since the total distance is

420

miles and the target average speed is

60

mph, the total time must be

7

hours. The first leg took

3

hours, leaving

4

hours for the remainder of the trip. The remaining distance is

180

miles (

420 - 240

). Dividing the remaining

180

miles by the remaining

4

hours gives the required speed of

45

mph.

Adım Adım Çözüm

1

Calculate the total time allowed for the entire mission.

Total Time =

420 \text{ miles} \div 60 \text{ mph} = 7 \text{ hours}

.

Overall average speed requires knowing the total allowable time, which is found by dividing the total distance by the target average speed.

2

Determine the remaining distance to be covered.

Remaining Distance =

420 \text{ miles} - 240 \text{ miles} = 180 \text{ miles}

.

Subtract the distance traveled during the first leg from the total mission distance.

3

Determine the remaining time available.

Remaining Time =

7 \text{ hours} - 3 \text{ hours} = 4 \text{ hours}

.

Subtract the time spent on the first leg from the total allowable mission time.

4

Calculate the required average speed for the remaining distance.

Required Speed =

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

.

Speed is calculated by dividing the remaining distance by the remaining time.

Anahtar Kavram

Average Speed

Soru 58Soru →

A high-speed passenger train is scheduled to travel a $300$ -mile route between two cities with an overall average speed of $60$ miles per hour. During the first leg of the trip, the train travels $150$ miles at an average speed of $50$ miles per hour. At what average speed must the train travel for the remaining $150$ miles to meet its scheduled overall average speed?

75 mph

70 mph

100 mph

30 mph

Cevabı ve açıklamayı göster

Cevap: 75 mph

Cevap

The train must travel at 75 mph for the remaining distance.

To solve for the required speed, you must work with time. The entire 300-mile trip at an average of 60 mph allows a total of 5 hours (

300 \div 60 = 5

). The first 150 miles at 50 mph consumed 3 hours (

150 \div 50 = 3

). This leaves exactly 2 hours to cover the remaining 150 miles. Dividing the remaining distance by the remaining time (

150 \div 2

) gives the necessary speed of 75 mph.

Adım Adım Çözüm

1

Calculate the total time allowed for the entire trip.

300 \text{ miles} \div 60 \text{ mph} = 5 \text{ hours}

Average speed is defined as total distance divided by total time. We need the total time limit to figure out how much time is left.

2

Calculate the time spent on the first leg of the trip.

150 \text{ miles} \div 50 \text{ mph} = 3 \text{ hours}

Using the distance and speed given for the first segment, we determine how much of our total time budget has been used.

3

Determine the time remaining for the second leg.

5 \text{ hours} - 3 \text{ hours} = 2 \text{ hours}

Subtracting the time already used from the total allowed time gives the time remaining to complete the journey.

4

Calculate the required average speed for the remaining distance.

150 \text{ miles} \div 2 \text{ hours} = 75 \text{ mph}

Speed is distance divided by time. Applying this to the remaining segment gives the required speed.

Anahtar Kavram

To find an unknown speed in a multi-segment trip, you must base calculations on Total Distance and Total Time, rather than averaging the individual speeds.

Soru 59Soru →

A military supply convoy is tasked with delivering equipment to an outpost $210$ miles away. The convoy commander is ordered to maintain an overall average speed of $35$ miles per hour for the entire journey. If the convoy completes the first $90$ miles in $2$ hours, what average speed, in miles per hour, must they maintain for the remainder of the trip to exactly meet their overall time target?

Cevabı ve açıklamayı göster

Cevap: 30

Cevap

The convoy must maintain a speed of 30 mph for the remainder of the trip.

The overall target requires the

210

-mile trip to be completed in

6

hours (

210 \div 35

). Because the first

90

miles took

2

hours, there are

120

miles left to travel and

4

hours remaining to do so. Therefore, the required speed is

120

miles

\div

4

hours =

30

mph.

Adım Adım Çözüm

1

Calculate the total allowable time for the convoy's trip.

Total time =

210 \div 35 = 6

hours.

Overall average speed is the total distance divided by total time. Knowing the total distance and target average speed allows us to find the total time allowed.

2

Calculate the remaining distance for the second part of the trip.

Remaining distance =

210 - 90 = 120

miles.

We need to find out how much further the convoy has to travel.

3

Calculate the remaining time available to complete the journey.

Remaining time =

6 - 2 = 4

hours.

Subtracting the time already spent from the total time gives the time left to cover the remaining distance.

4

Calculate the required average speed for the final leg.

Required speed =

120 \div 4 = 30

mph.

Average speed for any leg is the distance of that leg divided by the time spent on that leg.

Anahtar Kavram

Average speed is calculated by dividing the total distance by the total time, and the properties of individual legs (distance and time) sum to the total distance and total time.

Soru 60Soru →

A Coast Guard maritime patrol aircraft is assigned a $720$ -mile patrol route. To meet mission parameters, the aircraft must maintain an overall average speed of $180$ miles per hour from start to finish. The crew completes the first $480$ miles at a cruising speed of $320$ miles per hour, then lands at a coastal airfield for a $30$ -minute refueling stop. What average speed must the aircraft maintain during the final leg of the patrol to achieve the required overall average speed?

40 mph

80 mph

100 mph

120 mph

Cevabı ve açıklamayı göster

Cevap: 120 mph

Cevap

The aircraft must maintain an average speed of

120

mph for the final leg.

The correct answer is found by first determining the total mission time (

720 \div 180 = 4

hours). Next, find the time used for the first leg (

480 \div 320 = 1.5

hours) and add the

30

-minute (

0.5

hour) stop, meaning exactly

2.0

hours have elapsed. Subtracting this from the total time gives

2.0

hours remaining to cover the final

240

miles. Dividing

240

miles by

2.0

hours yields exactly

120

mph.

Adım Adım Çözüm

1

Calculate the total time allowed for the entire mission.

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

Overall average speed equals total distance divided by total time.

2

Calculate the time spent flying the first leg.

480 \text{ miles} \div 320 \text{ mph} = 1.5 \text{ hours}

(or

1

hour and

30

minutes)

Time equals distance divided by speed.

3

Calculate the total time used so far, including the refueling stop.

1.5 \text{ hours} + 0.5 \text{ hours} = 2.0 \text{ hours}

The

30

-minute refueling stop must be added to the flight time to find the total elapsed time.

4

Determine the remaining time available for the final leg.

4.0 \text{ hours} - 2.0 \text{ hours} = 2.0 \text{ hours}

Subtracting the elapsed time from the total allowed time gives the time limit for the remainder of the trip.

5

Determine the remaining distance to travel.

720 \text{ miles} - 480 \text{ miles} = 240 \text{ miles}

Subtracting the distance already covered from the total distance gives the remaining distance.

6

Calculate the required average speed for the final leg.

240 \text{ miles} \div 2.0 \text{ hours} = 120 \text{ mph}

Speed equals distance divided by time.

Anahtar Kavram

To find a required average speed for a remaining segment, subtract the distance already traveled from the total distance, subtract the time already spent (including stops) from the total allowed time, and divide the remaining distance by the remaining time.

Time, Rate, and Distance

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