A swimmer makes a round trip up and down the river which takes her X

Question

A swimmer makes a round trip up and down the river which takes her X hours. If the next day she swims the same distance with the same speed in still water, which takes her Y hours, which of the following statements is true?

(A) X > Y
(B) X < Y
(C) X = Y
(D) X = Y/2
(E) Cannot be determined

Show Answer

Official Answer

A

(A) X > Y
(B) X < Y
(C) X = Y
(D) X = Y/2
(E) Cannot be determined

siddhantvarma · Answer

Encountered this question in the GMAT Club Quant Flashcards.

OFFICIAL EXPLANATION:

Pick numbers and then check them against the options. Take 12 km as the distance traveled up/down the river, and assume the swimmer's speed to be 4 km/h; the current being 2 km/h, which means 6 km/h down the river and 2 km/h up the river. Going upriver takes 2 hours, returnjourney takes 6, thus a total of 8 hours. In still
water, 24 km requires 6 hours. Thus X=8 and Y=6. Plug these into the answer choices. (8 > 6).   The correct answer is A

Alternate Explanation:

Let's say the distance one way is d miles
The swimmer's speed in still water is v miles/hour
The river's current speed is c miles/hour

For the river swim (taking X hours total):
Upstream speed = v - u (swimming against current)
Downstream speed = v + u (swimming with current)
Time upstream = d/(v-u)
Time downstream = d/(v+u)
Total time X = d/(v-u) + d/(v+u) => X = 2dv/( v^2 - u^2 )

Y = 2d/v

Comparing the denominators:
X has denominator  v^2 - u^2 
Y has denominator v

Since  v^2 - u^2  < v2 (because u > 0), we know that X > Y

Therefore X > Y is the correct answer.

This makes intuitive sense because swimming against the current for half the journey slows you down more than swimming with the current speeds you up for the other half, making the river journey take longer overall than the still-water journey.

MalachiKeti · Answer

Pls explain the comparing denominators part? 
V^2-U^2 is less than V just because U is subtracted?? What is V is bigger number such that squaring makes it big?

Also isn't number taking risky? What is there exists other cases were it cannot be determined..

skry209 · Answer

X = 2dv/ v^2 - u^2 
Y = 2d/v 
Multiply numerator and denominator of Y by v => Y = 2dv/v^2
Both the numerators of X and Y are same. Where as the denominator of X, Y are v^2-u^2 and v^2, 
since v,u >0, v^2 > v^2 - u^2 => X > Y

A swimmer makes a round trip up and down the river which takes her X

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GMAT Problem Solving (PS) Questions

A swimmer makes a round trip up and down the river which takes her X

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