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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
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Re: Cindy paddles her kayak upstream at m kilometers per hour [#permalink] New post 25 Jan 2015, 02:56
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Re: Cindy paddles her kayak upstream at m kilometers per hour [#permalink] New post 25 Jan 2015, 13:21
Expert's post
Hi All,

This question involves the Distance Formula and can be solved by TESTing VALUES.

Distance = (Rate)(Time)

We're told a few things about a kayaker:

1) She travels upstream at M km/hour
2) She travels downstream at N km/hour
3) Total TIME traveled is P hours

We're asked for the DISTANCE traveled UPSTREAM....

For this question, we're going to choose the two speeds AND the distance traveled....this will help us figure out the time traveled in each direction (and thus, the TOTAL TIME).

M = 2 km/hour upstream
N = 3 km/hour downstream
Distance = 6 km in each direction

Upstream:
D = (R)(T)
6km = (2km/hour)(T)
6/2 = T
T = 3 hours upstream

Downstream:
D = (R)(T)
6km = (3km/hour)(T)
6/3 = T
T = 2 hours downstream

P = TOTAL Time = 5 hours

We're asked for the DISTANCE traveled upstream, so we're looking for an answer that = 6 when M = 2, N = 3 and P = 5.

Answer A: (M)(N)(P) = (2)(3)(5) = 30 NOT a match
Answer B: MN/P = (2)(3)/(5) = 6/5 NOT a match
Answer C: (M+N)/P = (2+3)/5 = 5/5 NOT a match
Answer D: MNP/(M+N) = 30/5 = 6 This IS a MATCH
Answer E: PM/N - PN/M = 10/3 - 15/2 = Negative NOT a match

Final Answer:
[Reveal] Spoiler:
D


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Re: Cindy paddles her kayak upstream at m kilometers per hour   [#permalink] 25 Jan 2015, 13:21
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