Question 174234
Here's one approach to these types of problems:
Find the "rate" at which each person can do the job.
For the house-painting job, we'll find how much of the house can be painted by each participant in 1 hour.
If Sally can paint the house in 4 hours, then she can paint 1/4 of the house in 1 hour.
If John can paint the house in 6 hours, then he can paint 1/6 of the house in 1 hour. So, together, they can paint 1/4 + 1/6 = 5/12 of the house in 1 hour.
If the two of them can paint 5/12 of the house in 1 hour, then it will take them 12/5 hours to paint the house.
12/5 = 2 2/5 hours = 2 hours and 24 minutes.
Similarly for the second problem, find the "rate" at which each person can fill the pool.
Jim can fill the pool in 30 minutes, so he can fill 1/30 of the pool in 1 minute.
Sue can fill the pool in 45 minutes, so she can fill 1/45 of the pool in 1 minute.
Tony can fill the pool in 90 minutes (1 1/2 hrs), so he can fill 1/90 of the pool in 1 minute.
Working together, they can fill (1/30 + 1/45 + 1/90 = 6/90 = 1/15) of the pool in 1 minute, so it would take them 15/1 = 15 minutes to fill the pool together.