Question

Jim can fill a pool carrying buckets 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?

Answer 1

In a problem like this, we need to know what is the fraction of work each achieves in a unit time, say a minute.

If all three work together, add up the fraction of work they can do in one minute. The reciprocal is the time required in minutes.

Each minute, Jim can do 1/30th of the work, and Sue 1/45.
If the two of them work together, they can finish (1/30+1/45)=5/90=1/18 of the work in one minute. Therefore they would finish the work in 18 minutes.

Solve the same way when Tony chips in.