Question 107438: 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 1/2 hours. How quickly can all three fill the pool together?
Found 2 solutions by ankor@dixie-net.com, bucky:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 1/2 hours. How quickly can all three fill the pool together?
:
Let t = time required if they work together
Let 1 = the full pool
Convert 1.5 hrs to minutes: 90 min
A simple equation:
Multiply equation by 90, this gets rid of the denominators;
You then have
3t + 2t + t = 90
6t = 90
t = 90/6
t = 15 minutes working together:
:
Check solution:
15/30 + 15/45 + 15/90 =
1/2 + 1/3 + 1/6 =
3/6 + 2/6 + 1/6 = 1
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! Here's one way of looking at the problem:
.
First, since Jim can fill the pool in 30 minutes, this means that for each minute he fills
 of the pool.
.
Next, since Sue can fill the pool in 45 minutes, this means that in one minute she fills
 of the pool.
.
Finally, since Tony can fill the pool in 90 minutes (90 minutes = 1 1/2 hours) for each minute
he works, he fills  of the pool.
.
Then for each minute that they work together their total contribution to filling the pool is
the sum of their individual contributions ... 
.
90 is the least common denominator. Convert the fractions so they all have 90 as the denominator.
When you do, the sum becomes:
.
.
and 6 is a common factor of both the numerator and denominator of  . Therefore,
.
This shows that when Jim, Sue, and Tony work together that each minute they fill  of the
pool. Therefore, in 15 minutes they will fill the pool.
.
In equation form this becomes:
.
.
where the 1 on the right side represents 1 pool full and T is the unknown number of minutes
that it takes to fill 1 pool.
.
When you combine the three fractions as we did previously this equation becomes:
.
.
Solve for T by either dividing both sides of this equation by or by multiplying
both sides by 15 to get:
.
.
and since we were working in units of minutes, the answer for filling the pool when all
three persons work together is T = 15 minutes.
.
Another way of looking at the problem is to find a common number of minutes that is divisible
by 30, 45, and 90. That number is 90. Then look at it this way ... in 90 minutes Jim would
fill the pool 3 times, Sue would fill it twice, and Tony would fill it once. Therefore,
if all three worked together, they would fill the pool a total of 6 times in 90 minutes. So
to find how long it takes to fill the pool once, divide 90 minutes by 6 times and you
get 15 minutes ... the same answer as we got previously.
.
Hope this helps you to understand how to do the problem.
.
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