Cindy paddles her kayak upstream at m kilometers per hour

Question

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. \(\frac{pm}{n} - \frac{pn}{m}\)

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

Bunuel · Accepted Answer

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.

WholeLottaLove · Answer

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. \(\frac{pm}{n} - \frac{pn}{m}\)

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

EMPOWERgmatRichC · Answer

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

robu · Answer

Sir , will we not consider any value for speed of current/river.?
Pls. clarify. thanks in advance.

CounterSniper · Answer

let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/m
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/m)+(d/n)
 =d(m+n)/mn
d=pmn/(m+n)

mvictor · Answer

i put d for distance.
first leg time: d/m 
second leg time : d/n 
d/m + d/n = p
d*(m+n)/nm = p
d=pnm/(m+n)

ppcm · Answer

A. mnp not equal to a distance
B. mn/p not equal to an acceleration
C. (m + n)/p not equal to a distance
D. mnp/(m + n) equal to a distance 
E. pm/n- pn/m equal to a time

Then answer is D

ScottTargetTestPrep · Answer

We can let the distance upstream = d and the distance downstream = d. Since the rate going upstream was m kmh and the distance going downstream was n kmh, and time = distance/rate, the time going upstream was d/m and the time going downstream was d/n. We are also given that the total time was p hours. We can create the following equation and isolate d:

d/m + d/n = p

Multiplying by mn, we have:

dn + dm = mnp

d(n + m) = mnp

d = mnp/(n + m)

Answer: D

singhabhijeet · Answer

I have used below approach. Please suggest if this approach is correct.

Rate =  \frac{2 uv}{(u+v)}

u = rate with with person / object traveled from point A to point B.

v = rate with with person / object traveled from point B to point A.

Using above formula, 
Let distance between A to B be = d,
So, total distance = 2d.

R = \frac{2mn}{(m+n)}

Now,  D = R * T

=> 2d = \frac{2mn}{(m+n)}  * p

=> d = \frac{mnp}{(m+n)}

gracie · Answer

let t=upstream time
mt=upstream distance
mt=n(p-t)
t=np/(m+n)
mt=mnp/(m+n)
D

generis · Answer

Alternative method : assign numbers.

Start with distance and rate, then derive individual times. Add those times to get total time  p .

1. Assign values for distance and individual rates:

D  =  12 
 m  =  3  = upstream rate
 n  =  4  = downstream rate

2. Derive individual times,  D/r=t

Upstream  TIME: \frac{12}{3}  =  4

Downstream  TIME:  \frac{12}{4}  =  3

3. Add the times to get TOTAL time, which is  p

4 + 3 =  7

Plug  m=3, n=4, p=7  into answer choices. Only D works.

ScottTargetTestPrep · Answer

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

souvonik2k · Answer

Let d be the distance upstream or downstream
Total time = p
Sum of time taken upstream and downstream =  \frac{d}{m}  +  \frac{d}{n}  = p
  \frac{d(m+n)}{mn}  = p
d =  \frac{mnp}{(m+n)}

Answer D.

GMATXP · Answer

My solution:

The answer is a distance. The formula of the distance is d = speed * time.

I used the process of elimination looking at the 5 answers which one is a product of speed and time.

a. mnp is squared speed x time - NO
b. mn/p is squared speed divided by time - NO
c. m+n/p is speed divided by time - NO
d. mnp/m+n is squared speed x time divided by speed, which is speed x time - CAN BE RIGHT. We will now check the last one:
e. it is time + time, so NO

Which means D.

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Cindy paddles her kayak upstream at m kilometers per hour

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