SOLUTION: A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how lo

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how lo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 645397: A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how long will it take to fill the pool?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how long will it take to fill the pool?
In your head:
The LCM of 6 hours and 9 hours is 18 hours.  In 18 hours the fill-pipe will
fill the pool 3 times and the drain pipe will have drained it 2 times, so
that's 3-2 = 1 pool filled in 18 hours.  Answer: 18 hours.

By algebra.
The fill rate of the fill pipe is 1 pool per 6 hours or 1/6 pool per hour.
The "fill" rate of the drain pipe is the loss of one pool per 9 hours, or the
loss of 1/9 pool per hour, and we indicate a negative rate with a negative
sign, -1/9 pool per hour. The combined fill rate of both pipes is 1 pool per x
hours of 1/x pool per hour.  So the equation is gotten by equating the sum of
the fill rates to the combined fill rate: 

                  1/6 - 1/9 = 1/x

Multiply that through by 18x and solve to get 18 hours.

Edwin