Boat/Stream

Joy Shaha wrote:Q. A swimmer swims from point A against the current for 5 minutes and then swims backward with the current for next 5 minutes and comes to the point B. If AB = 100 meters, then the speed of the current in km/hr is?
a. 0.06 b. 0.2 c. 0.6 d. 1 e. None of these

Assume for simplicity that the swimmer swims at the same rate as the stream, call it X km/hr.

Therefore, swimming against the stream, he makes no upstream progress and remains at A.

Therefore, swimming with the current, his progress against ground is at the rate of 2X.

2X = .1km/(1/12) hr > X = 0.6 km/hr

Joy Shaha wrote:Q. A swimmer swims from point A against the current for 5 minutes and then swims backward with the current for next 5 minutes and comes to the point B. If AB = 100 meters, then the speed of the current in km/hr is?
a. 0.06 b. 0.2 c. 0.6 d. 1 e. None of these

Strange question. Is this a GMAT question? I guess we're supposed to assume her swimming speed is equal for both intervals? If so, regor60's answer is correct.

Another approach would be to assume she's a really, really slow swimmer - so slow in fact that her speed is 0. Then, all of the movement from point A to point B would be accomplished via the current. During the first 5 minutes, the current would push her back to some point x between A and B, and then during the next 5 minutes, the current would push her all the way back to point B. Since the current has moved her 100 meters in 10 minutes, the current's speed is 0.6 km/hr.

This looks like a question from India's CAT.

Assuming her speed is constant (a major but common assumption), we'd have

Against current:
Her rate = r
Current's rate = c
Effective rate = r - c
Time = 5

With current:
Her rate = r
Current's rate = c
Effective rate = r + c
Time = 5

The swimmer travels 5 * (r - c) meters AGAINST the current, then 5 * (r + c) meters WITH the current.

The difference between these is the distance backward that our swimmer has traveled, so

5 * (r + c) - 5 * (r - c) = 100

10c = 100

c = 10

So the current's rate is 10 meters per minute, or 600 meters per hour, or .6 kilometers per hour.