SOLUTION: An old pump takes 20 hours to drain a pool. A new pump takes 13 hours to drain the pool. How long will it take for both of them working together to drain the pool?

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Question 624895: An old pump takes 20 hours to drain a pool. A new pump takes 13 hours to
drain the pool. How long will it take for both of them working together to
drain the pool?
Found 2 solutions by unlockmath, Edwin McCravy:
Answer by unlockmath(1688)   (Show Source): You can put this solution on YOUR website!
Hello,
Looks like some data was omitted. Check the problem to see if you wrote it correctly.
RJ
Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!
The other tutor is right. Some information was omitted.  However,
I rewrote your original problem and made up the missing value:


An old pump takes 20 hours to drain a pool. A new pump takes 13 hours to
drain the pool.  How long will it take for both of them working together to
drain the pool?

Make this chart:

                   Mumber of             hours        Draining rate
                  Pools drained        required       in pools/hour
Old pump
New pump
Both together 

Let x = the number of hours it takes for both of them to drain the pool working
together.  Fill this in, as well as 29 hours for the old pump and 13 hours
for the new pump:

                   Mumber of             hours        Draining rate
                  Pools drained        required       in pools/hour
Old pump                                  20
New pump                                  13
Both together                              x  

In each of the three cases exactly 1 pool was drained, so we put 1 for the
number of pools drained in each case:  

                   Mumber of             hours        Draining rate
                  Pools drained        required       in pools/hour
Old pump                1                 20
New pump                1                 13
Both together           1                  x

Next we fill in the draining rates in pools/hour by diving the number of pools
drained by the hours.

                   Mumber of             hours        Draining rate
                  Pools drained        required       in pools/hour
Old pump                1                 20               1/20
New pump                1                 13               1/13
Both together           1                  x                1/x                


The equation comes from 

                  +  =  

                         +  = 


Get an LCD of 260x and multiply through

                        13x + 20x = 260
                              33x = 260
                                x = 
                                x = 
or about 7 hours 53 minutes.

Edwin
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