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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...

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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?

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

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.

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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.
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

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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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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: D

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

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Contact Rich at Rich.C@empowergmat.com

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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)

Answer: D

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Founder and CEO
scott@targettestprep.com



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