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# A math problem, pls help to solve it

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Manager
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Joined: 05 Jun 2011
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A math problem, pls help to solve it [#permalink]

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28 Jun 2011, 23:15
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(N/A)

Question Stats:

83% (02:23) correct 17% (03:41) wrong based on 6 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: My question
A is correct.. why???
[Reveal] Spoiler: OA
Manager
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Re: A math problem, pls help to solve it [#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
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Re: A math problem, pls help to solve it [#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

Intern
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Re: A math problem, pls help to solve it [#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
Manager
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Re: A math problem, pls help to solve it [#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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Re: A math problem, pls help to solve it   [#permalink] 29 Jun 2011, 18:09
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