SOLUTION: a particular pipe can fill a tank in 7 hours. when a second pipe is added, the tank can be filled in only 2 hours. how long would it take the second pipe to fill the tank by itself

                         
Make this chart, putting x for the hours required for the 2nd pipe alone,
since that's what we are to find:

                           number of        hours       rate in
                         tanks filled    required     tanks/hour     
-----------------------------------------------------------------
1st pipe alone
2nd pipe alone                               x
both pipes together

Fill in 7 for the hours required for the first pipe alone.
Fill in 2 for the hours required for both pipes together.


                           number of        hours       rate in
                         tanks filled    required     tanks/hour     
-----------------------------------------------------------------
1st pipe alone                               7
2nd pipe alone                               x
both pipes together                          2

In all cases exactly 1 tank was filled.  Therefore we put 1 for the number
of tanks that were filled in all three cases:

                           number of        hours       rate in
                         tanks filled    required     tanks/hour     
-----------------------------------------------------------------
1st pipe alone                1              7
2nd pipe alone                1              x
both pipes together           1              2
 
Fill in the three rates in tanks/hour by dividing the number of tanks 
filled (1) by the hours required:

                           number of        hours       rate in
                         tanks filled    required     tanks/hour     
-----------------------------------------------------------------
1st pipe alone                1              7            1/7
2nd pipe alone                1              x            1/x
both pipes together           1              2            1/2


The equation comes from

        +   =         
  

                   +  = 

Solve that and get x = 2.8 hours or 2 hours 48 minutes.

Edwin