Question 734433
 A pool has two pipes, A and B.
 The pool can be filled in 10 hours less by using pipe A than using pipe B.
 One day, pipe A was turned on for 10 hours before pipe B was also turned on.
 The pool was filled after 6 more hours.
 How long does it take pipe A alone to fill the pool?
:
let x = time required by pipe A alone
then
(x+10) = time required by pipe B alone
:
Let the completed job = 1 (a full pool)
:
A shared work equation, (pipe A on for 16 hrs):
{{{16/x}}} + {{{6/((x+10))}}} = 1
multiply by x(x+10) to clear the denominators, resulting in:
16(x+10) + 6x = x(x+10)
16x + 160 + 6x = x^2 + 10x
combine like terms to form a quadratic equation on the right:
0 = x^2 + 10x - 22x - 160
x^2 - 12x - 160 = 0
factors to
(x-20)(x+8) = 0
the positive solution
x = 20 hrs for pipe A to fill the tank
:
:
Check this
{{{16/20}}} + {{{6/30}}} = 
.8 + .2 = 1