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John has to make two round trips to the grocery store by the same rout

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John has to make two round trips to the grocery store by the same rout  [#permalink]

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New post 23 Jan 2018, 23:43
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A
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Difficulty:

  55% (hard)

Question Stats:

69% (02:47) correct 31% (02:03) wrong based on 56 sessions

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John has to make two round trips to the grocery store by the same route. On his initial trip to the store he travels at 20 miles per hour. He increases his speed on each of the following legs of the trip by 10 miles per hour. Which of the following is closest to his average speed in miles per hour for both round trips?

A. 31
B. 35
C. 39
D. 43
E. 44

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Re: John has to make two round trips to the grocery store by the same rout  [#permalink]

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New post 23 Jan 2018, 23:57
Bunuel wrote:
John has to make two round trips to the grocery store by the same route. On his initial trip to the store he travels at 20 miles per hour. He increases his speed on each of the following legs of the trip by 10 miles per hour. Which of the following is closest to his average speed in miles per hour for both round trips?

A. 31
B. 35
C. 39
D. 43
E. 44



A = 31

Total distance = D + D + D+ D
Total time = D/ 20 + D/30 + D/40 + D/50

Avg speed = Tot Distance / Tot time

= 31
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Re: John has to make two round trips to the grocery store by the same rout  [#permalink]

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New post 26 Jan 2018, 10:39
Bunuel wrote:
John has to make two round trips to the grocery store by the same route. On his initial trip to the store he travels at 20 miles per hour. He increases his speed on each of the following legs of the trip by 10 miles per hour. Which of the following is closest to his average speed in miles per hour for both round trips?

A. 31
B. 35
C. 39
D. 43
E. 44


We can let the distance between his house and the store = 60 miles.

For his first trip to store, his speed is 20 mph; thus, the time = 60/20 = 3 hours.

For his first return trip home, his speed is 30 mph; thus, the time = 60/30 = 2 hours.

For his second trip to store, his speed is 40 mph; thus, the time = 60/40 = 1.5 hours.

Finally, for his second return trip home, his speed is 50 mph; thus, the time = 60/50 = 1.2 hours.

Recall that average speed = (total distance traveled)/(total time), so we have:

Avg speed = (60 + 60 + 60 + 60)/(3 + 2 + 1.5 + 1.2)

Avg speed = 240/7.7

Avg speed = 31.17 ≈ 31 mph

Answer: A
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Re: John has to make two round trips to the grocery store by the same rout   [#permalink] 26 Jan 2018, 10:39
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