Let the time be x minutes.
their combined rate = 1 pool per x minutes or
their combined rate = 1/x pool per minute</b>
>>...Jim can fill a pool...in 30 minutes...<<
Jim's rate is 1 pool per 30 minutes or
Jim's rate = 1/30 pool per minute</b>
>>...Sue can do the same job in 45 minutes...<<
Sue's rate is 1 pool per 45 minutes or
Sue's rate = 1/45 pool per minute</b>
>>...Tony can do the same job in 1 ½ hours.,,<<
Tony's rate is 1 pool per 1½ hour
Tony's rate is 1 pool per 90 minutes
Tony's rate = 1/90 pool per minute
Jim's rate + Sue's rate + Tony's rate = their combined rate
1/30 + 1/45 + 1/90 = 1/x
Get the LCD of all the denominators 30, 45, 90, and x, which is 90x.
Multiply through by 90x
(90x)(1/30) + (90x)(1/45) + (90x)(1/90) = (90x)(1/x)
3x + 2x + x = 90
6x = 90
x = 90/6
x = 15 minutes
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