Question 107438
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 1/2 hours. How quickly can all three fill the pool together?
:
Let t = time required if they work together

Let 1 = the full pool

Convert 1.5 hrs to minutes: 90 min

A simple equation:
{{{t/30 + t/45 + t/90 = 1}}}

Multiply equation by 90, this gets rid of the denominators;
You then have
3t + 2t + t = 90

6t = 90
t = 90/6
t = 15 minutes working together:
:
Check solution:
15/30 + 15/45 + 15/90 =
1/2 + 1/3 + 1/6 =
3/6 + 2/6 + 1/6 = 1