SOLUTION: One cistern fill pipe is 7 times faster than another fill pipe. The faster cistern fill pipe takes 72 minutes less than the slower fill pipe. When will the cistern be full if bo

First we find their cistern-filling rates in cisterns per minuter.

Let the time required for the faster pipe to fill the cistern be x minutes
So the faster pipe's filling rate is 1 cistern per x minutes or
 or  cisterns per minute

Then the time required for the slower pipe to fill the cistern is x+72
minutes.  So the slower pipe's filling rate is 1 cistern per x+72 minutes 
or 
 or  cisterns per minute.

Since the faster pipe's rate is 7 times faster than the slower pipe's rate,
we have:

        
        
Cross-multiply:
      x + 72 = 7x
          72 = 6x
          12 = x

So the faster pipe's filling rate is  =  cistern per minute.
And the slower pipe's filling rate is  =  cistern per minute.

Now we have their respective filling rates in cisterns per minute.

Let t = the number of minutes required to fill the pipe when both pipes
are open.  So their combined filling rate is 1 cistern per t minutes 
or  or  cisterns per minute.

The equation comes from:

   

   

Multiply through by 84t

    7t + t = 84
        8t = 84
         t =  = 10.5 minutes.

Edwin