SOLUTION: Here is another problem i have been trying to figure out how to do. John can fill the pool in 30 min, Sue can fill the pool in 45 min, and Sam can fill it in 90 min how long woul

Algebra ->  Equations -> SOLUTION: Here is another problem i have been trying to figure out how to do. John can fill the pool in 30 min, Sue can fill the pool in 45 min, and Sam can fill it in 90 min how long woul      Log On


   

Question 186956: Here is another problem i have been trying to figure out how to do.
John can fill the pool in 30 min, Sue can fill the pool in 45 min, and Sam can fill it in 90 min how long would it take all three of them to fill the pool together?
I have the answer but dont know how to get the answer. I have asked everyone
I can think of for help including one of my teachers and still can't figure it
out.
I have figured out how much of the pool each can fill in 15 min which is half
the time it takes the fastest to fill the pool and several different ways but
can't figure out how to do it.
Found 3 solutions by Earlsdon, Alan3354, Edwin McCravy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Think about find the rate at which each person can fill the pool.
If John can fill the pool in 30 minutes, then he can fill 1%2F30 in 1 minute.
If Sue can fill the pool in 45 minutes, then she can fill 1%2F45 of the pool in 1 minute.
If Sam can fill the pool in 90 minutes, then he can fill 1%2F90 of the pool in 1 minute.
So if they work together, then all three of them can fill 1%2F30+%2B+1%2F45+%2B+1%2F90 of the pool in 1 minute.
Adding these fractions, you find that the three of them can fill 1%2F15 of the pool in 1 minute.
Well, if they can fill 1%2F15 of the pool in 1 minute, then it will take them 15 minutes to fill the entire pool working together.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
here is another problem i have been trying to figure out how to do.
john can fill the pool in 30 min, sue can fill the pool in 45 min, and sam can fill it in 90 min how long would it take all three of them to fill the pool together
------------------------
You have to find how much of the pool each can fill in a minute, then add those.
John can fill 1/30 per minute, sue 1/45 and sam 1/90
1/30 + 1/45 + 1/90 = 6/90 = 1/15 of the pool per minute together
Then, it takes 15 minutes.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:

Make this chart


       Number of pools filled = Rate in pools per minute  × Time required
John  |                       |                           | 
Sue   |                       |                           |   
Sam   |                       |                           |
-------------------------------------------------------------------------
All 3 |                       |                           | 

Since the question asks:

>>...How long would it take all three of them to fill the pool together?...<< 

We let T represent the time required for all 3 to fill it, so we put 
x in the bottom right position in the table, for that's the time for
all 3.  We also fill in 1 for the number of pools 

       Number of pools filled = Rate in pools per minute  × Time required
John  |                       |                           | 
Sue   |                       |                           |   
Sam   |                       |                           |
-------------------------------------------------------------------------
All 3 |          1            |                           |       x

>>...John can fill the pool in 30 min...<<

So that's 1 pool, so we put in 1 for the number of pools that John
fills, and we put in 30 for his time required to fill that 1 pool: 

       Number of pools filled = Rate in pools per minute  × Time required
John  |          1            |                           |      30
Sue   |                       |                           |   
Sam   |                       |                           |
-------------------------------------------------------------------------
All 3 |          1            |                           |       x

>>...Sue can fill the pool in 45 min...<< 

So that's 1 pool, so we put in 1 for the number of pools that Sue
fills, and we put in 45 for her time required to fill that 1 pool:

       Number of pools filled = Rate in pools per minute  × Time required
John  |          1            |                           |      30
Sue   |          1            |                           |      45 
Sam   |                       |                           |
-------------------------------------------------------------------------
All 3 |          1            |                           |       x

>>...Sam can fill it in 90 min...<<

So that's 1 pool, so we put in 1 for the number of pools that Sam
fills, and we put in 90 for his time required to fill that 1 pool: 


       Number of pools filled = Rate in pools per minute  × Time required
John  |          1            |                           |      30
Sue   |          1            |                           |      45 
Sam   |          1            |                           |      90
-------------------------------------------------------------------------
All 3 |          1            |                           |       x

Next we fill in the rates by this formula:

Rate =  (Number of pools filled)/(Time required)

That is we put the number of pools filled over the time:


       Number of pools filled = Rate in pools per minute  × Time required
John  |          1            |           1/30            |      30
Sue   |          1            |           1/45            |      45 
Sam   |          1            |           1/90            |      90
-------------------------------------------------------------------------
All 3 |          1            |            1/x            |       x 

Now the rate for all three must equal the sum of their rates.
So we have the equation

                  1/30 + 1/45 + 1/90 = 1/x

                1%2F30%2B1%2F45%2B+1%2F90+=+1%2Fx

Now to clear of fractions, we multiply every term through by the 
LCD of 90x

                90x%281%2F30%29%2B90x%281%2F45%29%2B+90x%281%2F90%29+=+90x%281%2Fx%29

                 3x%2B2x%2Bx=90
                        
                      6x=90

                        x=15                            

So it would take all three 15 minutes.

Edwin