SOLUTION: There is a pool of water. One Pipe empties the pool in 45 minutes. The other pipe empties it in 67.5 minutes. How long would it take to empty the pool if both pipes were used to

Question 107298: There is a pool of water. One Pipe empties the pool in 45 minutes. The other pipe empties it in 67.5 minutes. How long would it take to empty the pool if both pipes were used together?
This is from a worksheet my son brought home.
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
each pipe empties some fraction of the pool ... the fraction is the combined time divided by the individual time

example: if a pipe took 60 minutes and the combined time was 20 minutes,
... then the pipe would have emptied 20/60 or 1/3

let x="combined time" ... (x/45)+(x/67.5)=1 ... multiplying by 135 gives 3x+2x=135
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the two pipes be labeled pipe A and pipe B, just for convenience.
First, we'll find the rate that each pipe empties the water from the pool.
If pipe A can empty the pool in 45 minutes, then it can empty 1/45 of the pool in 1 minute.
If pipe B can empty the pool in 67.5 minutes, then it can empty 1/67.5 of the pool in 1 minute.
Now we can find out how much of the pool can be emptied in 1 minute if both pipes are used together.
=
So with both pipes in use, they can empty 1/27 of the pool in 1 minute.
So if we multiply 1/27 by 27 we'll find out how many minutes it takes to empty the entire pool.
1/27 of the pool = 1min.
The entire pool = 27 mins.
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