SOLUTION: I'm not sure if this goes under "Combinatorics", as I've never heard of that term before, but here goes.. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do

Question 307255: I'm not sure if this goes under "Combinatorics", as I've never heard of that term before, but here goes..
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?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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?
.
First, convert all rates to hours:
Jim: 1 pool per 30 min = 1 pool per .5 hour = 1/.5
Sue: 1 pool per 45 min = 1 pool per .75 hour = 1/.75
Tony: 1 pool per 1.5 hour = 1/1.5
.
Let t = time for all three to fill pool
then
t(1/.5 + 1/.75 + 1/1.5) = 1
Multiplying both sides by 1.5:
t(3 + 2 + 1) = 1.5
6t = 1.5
t = 1.5/6
t = 0.25 hours
OR
t = 15 minutes

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