SOLUTION: Jim can fill a pool in 30 min. Sue can fill the same pool in 45. Tony can fill the pool in an hour and a half. How quickly can they fill it together?

Algebra ->  Functions -> SOLUTION: Jim can fill a pool in 30 min. Sue can fill the same pool in 45. Tony can fill the pool in an hour and a half. How quickly can they fill it together?      Log On


   

Question 124547: Jim can fill a pool in 30 min. Sue can fill the same pool in 45. Tony can fill the pool in an hour and a half. How quickly can they fill it together?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Think of it this way.
.
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.
.
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.
.
When they all work together each minute that goes by they fill the sum of all these rates.
So in a minute they fill:
.
1%2F30+%2B+1%2F45+%2B+1%2F90
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of the pool. If you put all of these fractions over a common denominator of 90 you get:
.
3%2F90+%2B+2%2F90+%2B+1%2F90+=+6%2F90+=+1%2F15
.
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:
.
%281%2F30+%2B+1%2F45+%2B+1%2F90%29%2At+=+1
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Again, combining the fractions results in:
.
%281%2F15%29%2At+=+1
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You can solve for t by either dividing both sides of this equation by 1%2F15 or by multiplying
both sides of the equation by 15. In either case you will get:
.
t+=+15
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Indicating that the pool gets filled in 15 minutes when they all work together.
.
Hope this helps you to understand the problem a little better.
.