SOLUTION: An inlet pipe can fill a water tank in 10 hours, while an outlet pipe can empty the same tank in 15 hours. By mistake, both pipes are left open. How long will it take to fill the w

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Question 451162: An inlet pipe can fill a water tank in 10 hours, while an outlet pipe can empty the same tank in 15 hours. By mistake, both pipes are left open. How long will it take to fill the water tank with both pipes open?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
An inlet pipe can fill a water tank in 10 hours, while an outlet pipe can empty the same tank in 15 hours. By mistake, both pipes are left open. How long will it take to fill the water tank with both pipes open?
Two ways to do it.

In your head:

The LCM of 10 hours and 15 hours is 30 hours. So in 30 
hours the inlet pipe has filled 3 tanks and the outlet 
pipe has emptied 2 tanks. So that amounts to 1 tank 
being filled in 30 hours.

Answer: 30 hours.

---------------------------------------------

By algebra:  

Let the answer be t.  Make this chart

                  tanks filled     time    rate in tanks/hour
Inlet pipe              1           10          
Outlet pipe            -1           15           
Both together           1            t           

Fill in the rates in tanks/hour by dividing the tanks filled by 
the time

                  tanks filled     time    rate in tanks/hour
Inlet pipe              1           10           1/10
Outlet pipe            -1           15          -1/15 
Both together           1            t           1/t 

The equation is formed by:

   Inlet pipe's rate + Outlet pipe's rate = Rate of both together

                           1/10 + (-1/15) = 1/t         

                              1/10 - 1/15 = 1/t

Multiply through by LCD = 30t

                                  3t - 2t = 30
                                        t = 30

Edwin
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