SOLUTION: Two pipes are used to to fill a water tank. The first pipe can fill the tank in 4 hours alone. The two
pipes can fill tank in 2 hours less time than the second time alone. How lon
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-> SOLUTION: Two pipes are used to to fill a water tank. The first pipe can fill the tank in 4 hours alone. The two
pipes can fill tank in 2 hours less time than the second time alone. How lon
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Question 1170603: Two pipes are used to to fill a water tank. The first pipe can fill the tank in 4 hours alone. The two
pipes can fill tank in 2 hours less time than the second time alone. How long will it take the
second pipe to fill the tank alone? Answer by greenestamps(13200) (Show Source):
(1) An informal solution, using a bit of insight with logical reasoning and simple arithmetic....
If the time required for the second pipe to fill the tank were also 4 hours, then the two pipes together could fill the tank in half the time, which is 2 hours. Since 2 hours working together is 2 hours less than the 4 hours for the second pipe alone, this satisfies the conditions of the problem.
ANSWER: 4 hours
(2) If a formal algebraic solution is requires....
Let x be the number of hours the second pipe takes to fill the tank alone.
Then the fraction of the tank filled by the first pipe in 1 hour is 1/4; the fraction filled by the second pipe in 1 hour is 1/x; and the fraction filled by both pipes together in 1 hour is 1/(x-2). So
Multiply the whole equation by the common denominator, :
or
Clearly the negative solution makes no sense in the problem, so the answer is x=4 hours.
