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 and a half hours. How quickly can all three fill the pool together?

Add the pool-filling RATES of the three people. That would be

2 pools/hour + (4/3) pools/hr + (2/3) pools/hour = 4 pools/hour

The time required to fill one pool when working together, assuming they do not get in each others' way, is
(1 pool)/(4 pools/hr) = 1/4 h = 15 minutes.

Ok I am still a little confused could you explain more about how you got the first part?

To get the pool filling RATE of each person, divide 1 by the time it takes to fill a pool, in hours. That is what I did. Then I added the three rates.

To find out how quickly all three can fill the pool together, we first need to determine how much of the pool each person can fill in 1 minute.

We can calculate this by taking the reciprocal of the time it takes for each person to fill the pool. For example, if Jim can fill the pool in 30 minutes, we can say that he can fill 1/30th of the pool in 1 minute.

So, let's calculate the rates of each person:

Jim's rate = 1 pool / 30 minutes = 1/30 pool per minute
Sue's rate = 1 pool / 45 minutes = 1/45 pool per minute
Tony's rate = 1 pool / (1.5 hours) = 1/90 pool per minute

To find the combined rate of all three, we simply add up their individual rates:

Combined rate = Jim's rate + Sue's rate + Tony's rate
= 1/30 + 1/45 + 1/90 pool per minute

To simplify this fraction, we can find a common denominator of 90:

Combined rate = (3/90) + (2/90) + (1/90) pool per minute
= 6/90 pool per minute
= 1/15 pool per minute

Therefore, all three of them together can fill 1/15th of the pool in 1 minute.

Hence, all three can fill the pool together in 15 minutes.