SOLUTION: 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 o
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-> SOLUTION: 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 o
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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?
PLEASE HELP! Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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): + = 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 + =
.8 + .2 = 1
