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Average speed

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Manager
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Joined: 05 May 2005
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Average speed [#permalink] New post 17 Aug 2007, 16:18
How would you solve?

A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

a) 4 4/5
b) 5
c) 5 1/5
d) 5 2/5
e) 5 3/5
VP
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Joined: 10 Jun 2007
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Re: Average speed [#permalink] New post 17 Aug 2007, 16:25
above720 wrote:
How would you solve?

A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

a) 4 4/5
b) 5
c) 5 1/5
d) 5 2/5
e) 5 3/5


A.

Uphill: 2 hour @ 4mph
Total distance = 4*2 = 8 miles
Down hill time: 1/6 * 8 = 4/3
Average Speed = Total Distance / Total Time = 16 / (2+4/3)
Avg Speed = 16 / (10/3) = 4 4/5.
Director
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Schools: University of Chicago, Wharton School
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Re: Average speed [#permalink] New post 17 Aug 2007, 16:28
above720 wrote:
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

a) 4 4/5
b) 5
c) 5 1/5
d) 5 2/5
e) 5 3/5


= (2x4 + 8) / (2 + 8/6)
= 16/ (20/6)
= 16x6/20
= 4 4/5


A.
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Re: Average speed [#permalink] New post 17 Aug 2007, 17:14
above720 wrote:
How would you solve?

A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

a) 4 4/5
b) 5
c) 5 1/5
d) 5 2/5
e) 5 3/5


This kind of problems(rate problems are explained in details in MGMAT Word Translations)
U should not just find the average of two given speed rates, the average speed is found by dividing the total distance by the total time to travel the distance.
First find the distance traveled by byciclist to town B S=t*v (t-time, v-speed) S = 2*4=8
now find the time spent for coming from b to a, t=S/v or t=8/6
So now Total time he spent in his trip to and from A is 2+(4/3) or 10/3
Total distance of trip is 2*8 or 16
so the average speed he travelled is 16/(10/3) or 4 4/5, A
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 [#permalink] New post 17 Aug 2007, 18:40
definitely A.

2 hours * 4mph = 8 miles each way
8 miles @ 6mph = 4/3 hour
so total trip was 16 miles in 10/3 hour (2 there, 4/3 back)
(16*3)/10 = 4.8

or 4 4/5 mph

A
  [#permalink] 17 Aug 2007, 18:40
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