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Time taken by Steamer to cross river

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by nikhilgmat31 » Thu Jun 04, 2015 12:53 am
A steamer which can travel at 10 miles per hour in still water starts from one end of the English Channel. How long will the steamer take to cross the 50 mile channel? The water currents are favorable for exactly the first half of the length of the channel and are unfavorable for the second half.
1.The water flows at a constant speed of 10/3 miles per hour.
2.The steamer's average speed during the second half of its trip is reduced to half of its average speed during the first half of its trip.
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jun 04, 2015 4:26 am
A better wording might be as follows:
nikhilgmat31 wrote:A steamer that travels at a constant speed of 10 miles per hour in still water starts from one end of the English Channel. If the steamer travels with the current for the first half of the trip and against the current for the second half of the trip, how long will the steamer take to cross the 50-mile channel?

1. For each half of the trip, the water flows at a constant speed of 10/3 miles per hour.
2. The average speed for the second 25 miles is equal to half the average speed for the first 25 miles.
Let c = the speed of the current.
Since the steamer travels WITH the current for the first half of the trip, the speed for the first half = (steamer speed) + (current speed) = 10 + c.
Since the steamer travels AGAINST the current for the second half of the trip, the speed for the second half = (steamer speed) - (current speed) = 10 - c.

Statement 1: For each half of the trip, the water flows at a constant speed of 10/3 miles per hour.
Since the value of c is known, the speed for each half of the trip can be determined, allowing us to calculate the total time for the entire trip.
SUFFICIENT.

Statement 2: The average speed for the second 25 miles is equal to half the average speed for the first 25 miles.
Thus:
(10 - c) = (1/2)(10 + c).
Since we can solve for c, the speed for each half of the trip can be determined, allowing us to calculate the total time for the entire trip.
SUFFICIENT.

The correct answer is D.
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