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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Cindy paddles her kayak upstream at m kilometers per hour... tagged by: AAPL ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Cindy paddles her kayak upstream at m kilometers per hour... 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? $$A.\ mnp$$ $$B.\ \frac{mn}{p}$$ $$C.\ \frac{m+n}{p}$$ $$D.\ \frac{mnp}{n+m}$$ $$E.\ \frac{pm}{n}-\frac{pn}{m}$$ The OA is D. Time upstream, T1 = d / m Time downstream T2 = d / n The total time will be, T1 + T2 = p. Then, I just need isolate d from, $$\frac{d}{m}+\frac{d}{n}=p\ -->d\left(\frac{n+m}{mn}\right)=p-->d=\frac{mnp}{m+n}$$ Is there a strategic approach to this question? Can any experts help, please? Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 AAPL 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? $$A.\ mnp$$ $$B.\ \frac{mn}{p}$$ $$C.\ \frac{m+n}{p}$$ $$D.\ \frac{mnp}{n+m}$$ $$E.\ \frac{pm}{n}-\frac{pn}{m}$$ The OA is D. Time upstream, T1 = d / m Time downstream T2 = d / n The total time will be, T1 + T2 = p. Then, I just need isolate d from, $$\frac{d}{m}+\frac{d}{n}=p\ -->d\left(\frac{n+m}{mn}\right)=p-->d=\frac{mnp}{m+n}$$ Is there a strategic approach to this question? Can any experts help, please? Thanks. You could pick some numbers. m = 10 km/h n = 20km/h Let's say it was a trip of 20 km. The upstream portion will take 2 hours at 10km/h and the downstream portion will take 1 hour at 20km/h, giving us a p of 2 + 1 = 3. Our target is 20 km. A) mnp = 10*20*3 --> nope B) mn/p = 10*20/3 --> nope C)(m + n)/p = (10 + 20)/3 =10 --> nope D) mnp/(n +m) = 10*20*3/(10 + 20) = 600/30 = 20. Yes! E)pm/n - pn/m = 3*10/20 - 3*20/10 = 30/20 - 60/10 --> nope. The answer is D _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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AAPL 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?

$$A.\ mnp$$
$$B.\ \frac{mn}{p}$$
$$C.\ \frac{m+n}{p}$$
$$D.\ \frac{mnp}{n+m}$$
$$E.\ \frac{pm}{n}-\frac{pn}{m}$$

The OA is D.

Time upstream, T1 = d / m

Time downstream T2 = d / n

The total time will be, T1 + T2 = p.

Then, I just need isolate d from,
$$\frac{d}{m}+\frac{d}{n}=p\ -->d\left(\frac{n+m}{mn}\right)=p-->d=\frac{mnp}{m+n}$$
Is there a strategic approach to this question? Can any experts help, please? Thanks.
Hi AAPL,

You have followed the correctly perfect approach to solve the problem.

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### GMAT/MBA Expert

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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

GMAT assassins aren't born, they're made,
Rich

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### GMAT/MBA Expert

GMAT Instructor
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AAPL 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?

$$A.\ mnp$$
$$B.\ \frac{mn}{p}$$
$$C.\ \frac{m+n}{p}$$
$$D.\ \frac{mnp}{n+m}$$
$$E.\ \frac{pm}{n}-\frac{pn}{m}$$
We can let distance upstream = distance downstream = d.

Thus:

d/m + d/n = p

Multiplying by mn, we have:

dn + dm = mnp

d(n + m) = mnp

d = mnp/(n + m)

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Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

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