SOLUTION: It takes 4 minutes longer to drain a Jacuzzi than it does to fill it. If the drain is left open, it takes 15 minutes to fill it. How many minutes does it take to fill the Jacuzzi w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes 4 minutes longer to drain a Jacuzzi than it does to fill it. If the drain is left open, it takes 15 minutes to fill it. How many minutes does it take to fill the Jacuzzi w      Log On


   

Question 689110: It takes 4 minutes longer to drain a Jacuzzi than it does to fill it. If the drain is left open, it takes 15 minutes to fill it. How many minutes does it take to fill the Jacuzzi when the drain is closed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes 4 minutes longer to drain a Jacuzzi than it does to fill it.
If the drain is left open, it takes 15 minutes to fill it.
How many minutes does it take to fill the Jacuzzi when the drain is closed?
:
Let x = time required to fill it (drain closed)
then
(x+4) = time required to drain it
:
Let the completed job = 1, (a filled jacuzzi)
+ is fill, - is drain
:
15%2Fx - 15%2F%28%28x%2B4%29%29 = 1
multiply by x(x+4) to clear the denominators, resulting in:
15(x+4) - 15x = x(x+4)
15x + 60 - 15x = x^2 + 4x
A quadratic equation
0 = x^2 + 4x - 60
Factors to
(x+10)(x-6) = 0
the positive solution is all we want here
x = 6 minutes to fill it with the drain closed
:
See if that checks out (10 min to drain it)
15%2F6 - 15%2F10 =
5%2F2 - 3%2F2 = 2%2F2 = 1