SOLUTION: Pipe A can fill a tank in five hours pipe B can fill it in two hours less than it takes pipe C, a drain pipe ,to empty the tank. with all three pipes open it takes three hours to f

Question 1129779: Pipe A can fill a tank in five hours pipe B can fill it in two hours less than it takes pipe C, a drain pipe ,to empty the tank. with all three pipes open it takes three hours to fill the tank. how long would it take pipe C to empty it?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
c, the time for pipe C to drain the tank if pipe C is working alone
c-2, time for pipe B to fill the tank if working alone

.
.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Pipe A's rate of filling:
[ 1 tank filled ] / [ 5 hrs ]
Let = time in hrs for pipe C to empty tank
pipe C's rate of emptying:
[ 1 tank emptied ] / [ t hrs ]
pipe B's rate of filling:
[ 1 take filled ] / [ t - 2 hrs ]
---------------------------------
Add rates for A % B
Subtract rate for C

Multiply both sides by

( choose positive time )
Pipe C empties the tank in 5 hrs
--------------------------------------
check:

OK

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Let x be the time for pipe C to empty the tank. Then the time for the pipe B to fill the tank is (x+2) hours. The rate of work for pipes A, B and C are , and of the tank volume per hour. The balance equation is + - = , or - = = = . To solve it, multiply both sides by 15*x*(x-2) and simplify step by step. You will get 15x - 15*(x-2) = 2x*(x-2) 30 = 2x^2 - 4x 2x^2 - 4x - 30 = 0 x^2 - 2x - 15 = 0 (x-5)*(x+3) = 0 Answer. x = 5 hours. Check. + - = of the tank volume. ! Correct !

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