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Cindy paddles her kayak upstream at m kilometers per hour

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Cindy paddles her kayak upstream at m kilometers per hour [#permalink] New post 30 Oct 2013, 06:57
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Cindy paddles her kayak upstream at m kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip ?

A. mnp

B. \frac{mn}{p}

C. \frac{m+n}{p}

D. \frac{mnp}{m+n}

E. \frac{pm}{n} - \frac{pn}{m}

Hi,

I'm having some troubles trying to resolve algebrically a ps question that i found on my kaplan book. The question is provided as an example about how to use "picking number" strategy, so in the book it's not solved algebrically; i've understood the explanation for solving it with picking numbers, nevertheless i want to be able to solve it with algebra.

Any hint ?
Thank you
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Oct 2013, 07:05, edited 3 times in total.
Edited the question and the OA.
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Re: Cindy paddles her kayak upstream at m kilometers per hour [#permalink] New post 30 Oct 2013, 07:15
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robertop wrote:
Cindy paddles her kayak upstream at m kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip ?

A. mnp

B. \frac{mn}{p}

C. \frac{m+n}{p}

D. \frac{mnp}{m+n}

E. \frac{pm}{n} - \frac{pn}{m}

Hi,

I'm having some troubles trying to resolve algebrically a ps question that i found on my kaplan book. The question is provided as an example about how to use "picking number" strategy, so in the book it's not solved algebrically; i've understood the explanation for solving it with picking numbers, nevertheless i want to be able to solve it with algebra.

Any hint ?
Thank you


Say the distance traveled upstream and downstream is d kilometers.

Time to cover d kilometers upstream = d/m hours.
Time to cover d kilometers downstream = d/n hours.

We are told that \frac{d}{m} + \frac{d}{n} = p --> d(\frac{n+m}{mn})=p --> d=\frac{mnp}{m+n}.

Answer : D.

Hope it's clear.
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Re: Cindy paddles her kayak upstream at m kilometers per hour [#permalink] New post 07 Nov 2013, 10:05
Cindy paddles her kayak upstream at m kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip ?

We are given p = total time so find the t1 and t2 to get to P.

The time to cover the distance upstream is d/m
The time to cover the distance downstream is d/n
t1+t2 = P (total time)

So, d/m+d/n = p
Take the d out and get the denominators to be the same.

d(n/nm + m/nm) = p
d(n+m / nm) = p

We are looking for d so isolate d:

d = nmp/n+m

D. mnp/m+n
Re: Cindy paddles her kayak upstream at m kilometers per hour   [#permalink] 07 Nov 2013, 10:05
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