Cindy paddles her kayak upstream at m kilometers per hour

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:

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

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

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)

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)

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

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

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


Rate = \(\frac{2 uv}{(u+v)}\) [Average rate formula used when distance traveled is same but rate is different]

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

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

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.

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

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.

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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