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

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): You can put this solution on YOUR website!

(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.

RELATED QUESTIONS
Two pipes are used to fill a water storage tank. The first pipe can fill the tank in 4... (answered by stanbon)

Two pipes are used to fill a water storage tank. The first pipe can fill the tank in 4... (answered by josmiceli)

Two pipes are used to fill a water tank. The first pipe can fill the tank in 4 hours. The (answered by mananth)

Two pipes together can fill a large tank in 10 hours. One of the pipes, used alone,... (answered by checkley77)

Two pipes together can fill a large tank in 10 hours. One of the pipes used alone takes... (answered by stanbon)

Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours (answered by stanbon)

two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours (answered by josgarithmetic)

Two pipes together can fill a large tank in 10 hours. One of the pipes, used alone, takes (answered by TimothyLamb)

I've tried to figure out what to use but for some reason it hasnt come to me. Please... (answered by scott8148)