Math and Arithmetic

Top Answer

15 min.

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

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