Question 7353
<font face = "courier new" size = 2>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 ½ hours. How quickly can
all three fill the pool together.</font>
<pre><b>
What we need is this equation:

Jim's rate + Sue's rate + Tony's rate = their combined rate
</b>
>>...How quickly can all three fill the pool together...<<
<b>
Let the time be x minutes. 
THEREFORE
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...<<
<b>TRANSLATION:
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...<<
<b>TRANSLATION:
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.,,<<
<b>TRANSLATION:
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
Now
Jim's rate + Sue's rate + Tony's rate = their combined rate
becomes
                       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
Edwin