Round Trips Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

A courier travels from the office to a client's location $40$ miles away. The trip there takes $1$ hour. The return trip along the same route takes $4$ hours due to heavy traffic. What is the courier's average speed for the entire round trip?

8

mph

10

mph

16

mph

25

mph

Cevabı ve açıklamayı göster

Cevap: $16$ mph

Cevap

16

mph

The correct answer is found by dividing the total distance for the round trip (

40

miles outbound +

40

miles return =

80

miles) by the total time taken (

1

hour +

4

hours =

5

hours). This gives an average speed of

80 \div 5 = 16

mph.

Adım Adım Çözüm

1

Calculate the total distance for the round trip.

40 + 40 = 80

miles

Average speed calculation requires the total distance traveled during the entire journey.

2

Calculate the total time for the round trip.

1 + 4 = 5

hours

Average speed calculation requires the total time elapsed.

3

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

80 \div 5 = 16

mph

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

Anahtar Kavram

The average speed for a round trip is calculated by dividing the total round-trip distance by the total time taken. It is not the simple arithmetic average of the speeds for each leg.

Soru 2Soru →

A delivery truck travels from a warehouse to a distribution center at an average speed of $40$ mph and returns along the same route at an average speed of $60$ mph. If the entire round trip takes $5$ hours, what is the total round-trip distance traveled by the truck?

120

miles

240

miles

250

miles

500

miles

Cevabı ve açıklamayı göster

Cevap: $240$ miles

Cevap

The correct total round-trip distance is

240

miles.

The total time is the sum of the time for each leg. Letting

d

be the one-way distance, the equation is

\frac{d}{40} + \frac{d}{60} = 5

. Solving this gives a one-way distance of

d = 120

miles. Since the question asks for the total round-trip distance, this must be doubled to get

240

miles.

Adım Adım Çözüm

1

Set up an equation for the total time of the trip.

Let

d

be the one-way distance. Time is equal to Distance divided by Speed. Therefore, the total time equation is

\frac{d}{40} + \frac{d}{60} = 5

.

The total round-trip time is the sum of the time spent on the outbound leg and the return leg.

2

Find a common denominator to add the fractions.

The least common multiple of

40

and

60

is

120

. Convert the fractions:

\frac{3d}{120} + \frac{2d}{120} = 5

.

Fractions must have a common denominator before they can be algebraically combined.

3

Combine the fractions and solve for the one-way distance

d

.

\frac{5d}{120} = 5

, which simplifies to

\frac{d}{24} = 5

. Multiplying both sides by

24

yields

d = 120

miles.

This isolates the variable

d

to determine the distance of a single leg of the journey.

4

Calculate the total round-trip distance.

Total distance =

2d = 2 \times 120 = 240

miles.

The question specifically asks for the total round-trip distance, which is twice the one-way distance.

Anahtar Kavram

To find distances in round trips with different speeds, set up an equation using the relationship Time = Distance / Speed for each leg, taking care to answer the specific question asked (one-way vs. total distance).

Tahmini Süre:1m 30s

Soru 3Soru →

A courier drives from a dispatch center to a client's location $60$ miles away and then returns to the dispatch center along the exact same route. The outbound drive to the client takes exactly $2$ hours. If the courier's average speed for the entire round trip is $24$ miles per hour, what is the courier's average speed on the return trip?

18

miles per hour

20

miles per hour

40

miles per hour

120

miles per hour

Cevabı ve açıklamayı göster

Cevap: $20$ miles per hour

Cevap

The courier's average speed on the return trip is

20

miles per hour.

To find the return speed, we first determine the total time of the trip. The total round-trip distance is

120

miles (

60

miles each way). Using the overall average speed of

24

mph, the total time is

120 \div 24 = 5

hours. Since the outbound trip took

2

hours, the return trip must have taken

5 - 2 = 3

hours. Finally, the return speed is the return distance (

60

miles) divided by the return time (

3

hours), which equals

20

miles per hour.

Adım Adım Çözüm

1

Calculate the total round-trip distance.

Total distance =

60 \times 2 = 120

miles.

The one-way distance is

60

miles, so the round trip is twice that amount.

2

Determine the total time taken for the entire round trip.

Total time =

120 \text{ miles} \div 24 \text{ mph} = 5

hours.

Average speed for the entire trip is total distance divided by total time.

3

Calculate the time taken for the return leg.

Return time =

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

hours.

The total trip time minus the outbound time gives the time remaining for the return trip.

4

Calculate the average speed for the return trip.

Return speed =

60 \text{ miles} \div 3 \text{ hours} = 20

miles per hour.

Speed is distance divided by time. The return distance is

60

miles and the return time is

3

hours.

Anahtar Kavram

Round Trip Average Speed

Soru 4Soru →

A ferry transports vehicles from the mainland to an island $18$ miles away. The ferry travels to the island at a speed of $9$ miles per hour and returns to the mainland along the same route at a speed of $6$ miles per hour.

How many hours does the complete round trip take?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The complete round trip takes 5 hours.

The round trip consists of two legs with different speeds. The outbound leg takes

18 \div 9 = 2

hours. The return leg takes

18 \div 6 = 3

hours. Adding these together yields a total time of

5

hours for the entire trip.

Adım Adım Çözüm

1

Calculate the time taken for the outbound trip.

18 \div 9 = 2

hours

Time is equal to distance divided by rate. This gives the time spent traveling to the island.

2

Calculate the time taken for the return trip.

18 \div 6 = 3

hours

The return trip covers the same distance but at a slower speed.

3

Calculate the total round-trip time.

2 + 3 = 5

hours

The total time for a round trip is the sum of the time spent on each individual leg.

Anahtar Kavram

Calculating total round-trip time by finding the time for each leg separately.

Soru 5Soru →

A cyclist travels from her home to a nearby town, a distance of $15$ miles, at an average speed of $12$ mph. On the return trip along the same route, her average speed is $20$ mph. What is her average speed, in mph, for the entire round trip?

Cevabı ve açıklamayı göster

Cevap: 15

Cevap

15

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

30

miles) by the total travel time (

2

hours), resulting in

15

mph.

Adım Adım Çözüm

1

Calculate the time for the outbound trip.

1.25 hours

Time equals distance divided by speed (

15 \text{ miles} / 12 \text{ mph} = 1.25 \text{ hours}

).

2

Calculate the time for the return trip.

0.75 hours

Time equals distance divided by speed (

15 \text{ miles} / 20 \text{ mph} = 0.75 \text{ hours}

).

3

Determine the total time and total distance for the entire round trip.

Total time = 2 hours, Total distance = 30 miles

Adding the outbound and return times (

1.25 + 0.75

) gives 2 hours. The round trip is twice the one-way distance (

15 \times 2

).

4

Calculate the average speed for the entire round trip.

15 mph

Average speed is total distance divided by total time (

30 \text{ miles} / 2 \text{ hours} = 15 \text{ mph}

).

Anahtar Kavram

Average Speed for a Round Trip

Soru 6Soru →

A pilot flies a cargo plane from Airport A to Airport B at an average speed of $240$ mph. The pilot returns along the exact same route, but due to a strong headwind, the return flight averages only $160$ mph. If the total flying time for the entire round trip was exactly $5$ hours, what is the one-way distance between Airport A and Airport B, in miles?

Cevabı ve açıklamayı göster

Cevap: 480

Cevap

480

By setting up an algebraic equation representing the total time taken for both legs of the trip (using Time = Distance / Speed), we get

d/240 + d/160 = 5

. Solving this equation by finding a common denominator of

480

yields

5d/480 = 5

, which simplifies to

d = 480

miles.

Adım Adım Çözüm

1

Define a variable for the unknown distance.

Let

d

be the one-way distance in miles.

We need to find the one-way distance and relate it to the given times and speeds.

2

Express the time for each leg of the trip using the formula Time = Distance / Speed.

Outbound time =

\frac{d}{240}

, Return time =

\frac{d}{160}

.

The total time is given, so we need mathematical expressions for the time of each individual leg.

3

Set up an equation for the total time.

\frac{d}{240} + \frac{d}{160} = 5

The sum of the outbound flight time and the return flight time equals the total round-trip flight time.

4

Find a common denominator to add the fractions.

The least common multiple of

240

and

160

is

480

. The equation becomes

\frac{2d}{480} + \frac{3d}{480} = 5

.

To solve for

d

, we must combine the fractional terms into a single term.

5

Solve the equation for

d

.

\frac{5d}{480} = 5 \Rightarrow 5d = 2400 \Rightarrow d = 480

.

Isolating

d

gives the final one-way distance.

Anahtar Kavram

Solving round trip scenarios by setting up a total time equation:

\frac{d}{v_1} + \frac{d}{v_2} = t_{total}

Tahmini Süre:2m 0s

Soru 7Soru →

A cyclist rides from his home to a nearby park $12$ miles away at a speed of $12$ miles per hour. He returns home along the same route at a speed of $6$ miles per hour. What is his average speed for the entire round trip in miles per hour?

9

4

8

24

Cevabı ve açıklamayı göster

Cevap: $8$

Cevap

The average speed for the entire round trip is

8

miles per hour.

The correct answer is found by first determining the total distance and total time. The park is 12 miles away, making the round trip 24 miles. The trip there takes 1 hour (12/12) and the trip back takes 2 hours (12/6), for a total of 3 hours. Dividing the total distance (24) by the total time (3) yields an average speed of 8 mph.

Adım Adım Çözüm

1

Calculate the total distance for the round trip.

12

miles (outbound) +

12

miles (return) =

24

total miles.

Average speed requires the total distance traveled over the entire journey.

2

Calculate the time taken for the outbound trip.

12

miles /

12

mph =

1

hour.

Time is equal to distance divided by speed.

3

Calculate the time taken for the return trip.

12

miles /

6

mph =

2

hours.

The cyclist travels the same distance back, but at a slower speed.

4

Calculate the total time for the trip.

1

hour +

2

hours =

3

total hours.

Average speed requires the total duration of the trip.

5

Calculate the average speed for the round trip.

24

miles /

3

hours =

8

miles per hour.

Average speed is equal to total distance divided by total time.

Anahtar Kavram

Average Speed for Round Trips

Soru 8Soru →

A cargo aircraft flies from a logistics hub to a regional airport, a one-way distance of $360$ miles. The aircraft makes the outbound journey at an average speed of $180$ mph. On the return trip along the exact same route, carrying a heavier load, it travels at an average speed of $120$ mph. What is the aircraft's average speed for the entire round trip?

72

mph

144

mph

150

mph

300

mph

Cevabı ve açıklamayı göster

Cevap: $144$ mph

Cevap

The correct average speed for the entire round trip is

144

mph.

The correct average speed is found by dividing the total round-trip distance by the total round-trip time. The total distance is

720

miles (

360

outbound

+ 360

return). The outbound flight takes

2

hours (

360 \div 180

) and the return flight takes

3

hours (

360 \div 120

), resulting in a total time of

5

hours. Dividing

720

miles by

5

hours gives an average speed of

144

mph.

Adım Adım Çözüm

1

Calculate the time taken for the outbound journey.

360

miles

\div 180

mph

= 2

hours.

Time equals distance divided by speed.

2

Calculate the time taken for the return journey.

360

miles

\div 120

mph

= 3

hours.

The return distance is the same, but the return speed is different.

3

Determine the total distance and total time for the entire round trip.

Total distance

= 360 + 360 = 720

miles. Total time

= 2 + 3 = 5

hours.

Average speed for a multi-leg journey requires the overall totals, not just the averages of each leg.

4

Calculate the overall average speed.

720

miles

\div 5

hours

= 144

mph.

Average speed is equal to the total distance divided by the total time.

Anahtar Kavram

Average Speed in Round Trips

Soru 9Soru →

A medical evacuation helicopter is dispatched from its base camp to pick up a patient at a rural hospital $120$ miles away. The pilot flies to the hospital at a steady speed of $120$ mph. Due to heavy headwinds on the way back, the helicopter's average speed for the entire round trip drops to $80$ mph. What is the helicopter's average speed, in mph, during the return flight?

Cevabı ve açıklamayı göster

Cevap: 60

Cevap

60

By finding the total trip time (3 hours) and subtracting the outbound time (1 hour), we determine the return trip took 2 hours to cover 120 miles. Dividing the 120-mile distance by the 2 hours yields an average return speed of 60 mph.

Adım Adım Çözüm

1

Calculate the total round-trip distance

240 miles

The one-way distance is 120 miles, so the full round trip is 120 + 120 = 240 miles.

2

Determine the total flight time

3 hours

Time equals total distance divided by the overall average speed (240 / 80 = 3).

3

Calculate the time taken for the outbound flight

1 hour

Time equals outbound distance divided by outbound speed (120 / 120 = 1).

4

Find the time taken for the return flight

2 hours

Return time is the total trip time minus the outbound trip time (3 - 1 = 2).

5

Calculate the average speed of the return flight

60 mph

Speed equals return distance divided by return time (120 / 2 = 60).

Anahtar Kavram

Average speed for a round trip is the total distance divided by the total time, not the arithmetic mean of the two different speeds.

Soru 10Soru →

A mountain rescue snowmobile is dispatched to retrieve a stranded hiker. It travels from base camp to the hiker's location at an average speed of $30$ miles per hour. Carrying the extra passenger on the return trip, the snowmobile heads back along the exact same trail at an average speed of $20$ miles per hour. If the total driving time for the entire rescue mission is $90$ minutes, what is the total round-trip distance traveled by the snowmobile?

18

miles

36

miles

37.5

miles

75

miles

Cevabı ve açıklamayı göster

Cevap: $36$ miles

Cevap

The total round-trip distance is

36

miles.

To find the total distance, we must use the relationship between distance, rate, and time. Because the one-way distances are equal, we can represent the one-way distance as

d

. The time for the outbound trip is

\frac{d}{30}

and the return trip is

\frac{d}{20}

. Their sum equals the total time of

1.5

hours (since

90

minutes is

1.5

hours). Solving

\frac{d}{30} + \frac{d}{20} = 1.5

yields

d = 18

. The round-trip distance is

2d

, which is

36

miles.

Adım Adım Çözüm

1

Convert the total driving time from minutes to hours.

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

Speed is given in miles per hour, so time must be consistent with these units.

2

Set up an equation representing the total time using the formula

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

. Let

d

represent the one-way distance.

\frac{d}{30} + \frac{d}{20} = 1.5

The total time is the sum of the time taken for the outbound trip and the time taken for the return trip.

3

Solve for the one-way distance (

d

) by finding a common denominator.

\frac{2d}{60} + \frac{3d}{60} = 1.5 \Rightarrow \frac{5d}{60} = 1.5 \Rightarrow \frac{d}{12} = 1.5 \Rightarrow d = 18 \text{ miles}

Solving the equation provides the distance for a single leg of the journey.

4

Calculate the total round-trip distance by multiplying the one-way distance by 2.

18 \times 2 = 36 \text{ miles}

The question asks for the total round-trip distance, which includes both the outbound and return legs.

Anahtar Kavram

Calculating distance for a round trip involving different speeds by setting up a total time equation.

Round Trips

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