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# Average speed

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Manager
Joined: 05 May 2005
Posts: 81
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Average speed [#permalink]  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
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 133 [0], given: 0

Re: Average speed [#permalink]  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
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 63 [0], given: 7

Re: Average speed [#permalink]  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.
VP
Joined: 09 Jul 2007
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Location: London
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Re: Average speed [#permalink]  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
Director
Joined: 12 Jul 2007
Posts: 865
Followers: 12

Kudos [?]: 218 [0], given: 0

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
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