Question 124547
Think of it this way. 
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Since Jim can fill the pool in 30 minutes, each minute that goes by he fills one-thirtieth (or 1/30)
of the pool.
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Sue can fill the same pool in 45 minutes. Therefore, each minute that goes by Sue fills one-forty fifth 
(or 1/45) of the pool.
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Tony fills the pool in and hour and a half (or 90 minutes). And so, each minute that goes by
he fills one-ninetieth (1/90) of the pool.
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When they all work together each minute that goes by they fill the sum of all these rates.
So in a minute they fill:
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{{{1/30 + 1/45 + 1/90}}} 
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of the pool. If you put all of these fractions over a common denominator of 90 you get:
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{{{3/90 + 2/90 + 1/90 = 6/90 = 1/15}}}
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So in one minute by working together they fill one-fifteenth of the pool.  Therefore, when
they work together they can completely fill the pool in 15 minutes. You can express this
in equation form as:
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{{{(1/30 + 1/45 + 1/90)*t = 1}}}
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Again, combining the fractions results in:
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{{{(1/15)*t = 1}}}
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You can solve for t by either dividing both sides of this equation by {{{1/15}}} or by multiplying
both sides of the equation by 15. In either case you will get:
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{{{t = 15}}}
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Indicating that the pool gets filled in 15 minutes when they all work together.
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Hope this helps you to understand the problem a little better.
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