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# A bicyclist travels uphill from town A to town B for 2 hours at an ave

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Manager
Status: Single
Joined: 05 Jun 2011
Posts: 119

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Location: Shanghai China
A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink]

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28 Jun 2011, 23:15
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:27) correct 12% (03:58) wrong based on 26 sessions

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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) 24/5
(b) 5
(c) 26/5
(d) 27/5
(e) 28/5
[Reveal] Spoiler: OA

Kudos [?]: 44 [0], given: 0

Manager
Joined: 19 Apr 2011
Posts: 106

Kudos [?]: 3 [0], given: 2

Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink]

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28 Jun 2011, 23:24
For the onward journey the distance travelled is 4*2 = 8 miles
backward journey same distance 8 miles and he travelled at 6 miles per hour so time taken = 8/6 = 4/3
Average speed = Total Disatance travelled/Total time taken
= 16/(2+4/3)
solving the above we get 24/5

e

Kudos [?]: 3 [0], given: 2

Director
Joined: 01 Feb 2011
Posts: 726

Kudos [?]: 143 [0], given: 42

Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink]

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29 Jun 2011, 16:51
from the uphill we can find out the distance = 4*2 = 8

average speed = total distance/total time

= 16/ (2+ (8/6)) = 24/5

Kudos [?]: 143 [0], given: 42

Intern
Joined: 14 Apr 2011
Posts: 18

Kudos [?]: 3 [0], given: 0

Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink]

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29 Jun 2011, 17:48
D=T*S
S=D/T
T=D/S

Su=speed uphill = 4mph
Sd=speed downhill=6mph
Tu=time spent biking uphill = 2 hrs
Du=Dd=Distance up or downhill = 4mph uphill * 2 hours = 8 miles one way
Td=Time spent biking downhill = Dd/Sd = 8/6 = 4/3

Average Speed = (Du + Dd) / (Tu + Td) = (8*2 ways) / (2 + 4/3)

= 24/5 so the answer is A

Kudos [?]: 3 [0], given: 0

Manager
Joined: 28 Feb 2011
Posts: 82

Kudos [?]: 41 [0], given: 2

Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink]

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29 Jun 2011, 18:09
There is an easy formula for return trips to calculate the average speed for the entire trip..

Let speeds be A and B

Avg= 2AB/(A+B)

In this case,

2x6x4/(6+4) = 24/5 mph
_________________

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Kudos [?]: 41 [0], given: 2

Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave   [#permalink] 29 Jun 2011, 18:09
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