SOLUTION: It takes pump A 2 hours less time than pump B to empty a certain swimming pool. Pump A is started at 8:00 A.M., and pump B is started at 11:00 A.M. If the pool is still half full

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Question 398521: It takes pump A 2 hours less time than pump B to empty a certain swimming pool. Pump A is started at 8:00 A.M., and pump B is started at 11:00 A.M. If
the pool is still half full at 5:00 P.M., then how long would it take pump A working alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes pump A 2 hours less time than pump B to empty a certain swimming pool.
Pump A is started at 8:00 A.M., and pump B is started at 11:00 A.M.
If the pool is still half full at 5:00 P.M., then how long would it take pump A working alone?
:
Let t = time required by pump A working alone
then
(t+2) = time required by pump B working alone
:
Pump A: 8 AM to 5 PM: 9 hrs,
Pump B: 11Am to 5 PM: 6 hrs
:
Let the empty pool = 1, then a half full pool = 1%2F2
:
9%2Ft + 6%2F%28%28t%2B2%29%29 = 1%2F2
Multiply by 2t(t+2), results:
9(2(t+2)) + 6(2t) = t(t+2)
18(t+2) + 12t = t^2 + 2t
18t + 36 + 12t = t^2 + 2t
30t + 36 = t^2 + 2t
A quadratic equation
t^2 + 2t - 30t - 36 = 0
t^2 - 28t - 36 = 0
Use the quadratic formula to find t
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: x=t; a=1; b=-28; c=-36
x+=+%28-%28-28%29+%2B-+sqrt%28-28%5E2-4%2Aa%2A-36+%29%29%2F%282%2A1%29+
Do the math here, should get a positive solution of:
t = 29.23 hrs, Pump A will empty the pool alone
:
:
Check solution
9%2F29.23 + 6%2F31.23 =
.308 + .192 = .500 (a half full pool)