<PRE><B>Question 169926</B>
Two pipes drain a waste holding tank in 8.00h. If used alone to empty the tank, one takes two hours longer than the other. How long does each take to empty the tank if used alone.
:
Let x = time for one pipe draining alone
then
(x+2) = time for the other pipe draining alone
:
Let the completed job (emptying the tank) = 1
:
{{{8/x}}} + {{{8/((x+2))}}} = 1
Multiply equation by x(x+2) to eliminate the denominators:
8(x+2) + 8x = x(x+2)
:
8x + 16 + 8x = x^2 + 2x
:
16x + 16 = x^2 + 2x
:
0 = x^2 + 2x - 16x - 16
A quadratic equation:
x^2 - 14x - 16 = 0
:
Find the positive value for x using the quadratic formula, you should get
x ~ 15.06 hrs</PRE>