Question

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?

The answer is 15 minutes. But how?


Figure the rate each can fill the pool
jim rate= 1/30 (1pool/30 min)
same relation for others.
The total rate then is the sum...

ratetotal=1/30 + 1/45 + 1/90

so we have one pool to do in this rate in some time T.

1= ratetotal*time

solve for time.


BobP answered this correctly, I thought I'd just answer it for the practice.
This kind of problem requires you to determine the individual rates, then add them to get a total answer. It looks like
1pool(1/30min + 1/45min + 1/90min) = 1pool (6/90min) = 1pool/15min
These kinds of problems are very common on tests for some reason. Change the numbers and try working another problem similar to this just for practice.

Answer 1

1/T = 1/t1 + 1/t2 + 1/t3.
1/T = 1/30 + 1/45 + 1/90,
1/T = 3/90 + 2/90 + 1/90 = 6/90,
T = 90/6 = 15 Min.