SOLUTION: Water can be pumped into or out of a tank via pipes A, B, and C. Pipe A can fill the tank in four hours. Pipe B in six hours. Pipe C can empty the tank in five hours. If the water

Question 516944: Water can be pumped into or out of a tank via pipes A, B, and C. Pipe A can fill the tank in four hours. Pipe B in six hours. Pipe C can empty the tank in five hours. If the water tank is empty and all three pipes begin opporating at the same time, how long will it take to fill the tank?

Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
Water can be pumped into or out of a tank via pipes A, B, and C. Pipe A can fill the tank in four hours. Pipe B in six hours. Pipe C can empty the tank in five hours. If the water tank is empty and all three pipes begin opporating at the same time, how long will it take to fill the tank?

Make this chart:

                         Number of          Time required     Rate in   
                        tanks filled           in hours      tanks/hour
Pipe A alone
Pipe B alone
Pipe C alone
All three together

Let x = the number of hours required for all three to fill one tank,
so fill in 1 for the number of tanks filled and x for the number of
hours:

                         Number of          Time required     Rate in   
                        tanks filled           in hours      tanks/hour
Pipe A alone
Pipe B alone
Pipe C alone
All three together           1                    x

Fill in 1 for the number of tanks filled for Pipes A and B.  Fill in
-1 for the number of pipes "filled" by Pipe C, since emptying one tank
is mathematically equivalent to "filling -1 tank":

                         Number of          Time required     Rate in   
                        tanks filled           in hours      tanks/hour
Pipe A alone                 1
Pipe B alone                 1
Pipe C alone                -1
All three together           1                    x

Fill in 4, 6, and 5 hours for time required for A, B, and C 

                         Number of          Time required     Rate in   
                        tanks filled           in hours      tanks/hour
Pipe A alone                 1                    4
Pipe B alone                 1                    6
Pipe C alone                -1                    5
All three together           1                    x


Fill in the four rates in tanks/hour by dividing the number of tanks
by the number of hours:

                         Number of          Time required     Rate in   
                        tanks filled           in hours      tanks/hour
Pipe A alone                 1                    4             1/4
Pipe B alone                 1                    6             1/6
Pipe C alone                -1                    5            -1/5 
All three together           1                    x             1/x

The equation comes from

(Pipe A's rate) + (Pipe B's rate) + (Pipe C's rate) = (All 3's rate)


                     +  +  = 

Solve that by first multiplying through by LCD = 60x

Asswer x = 60/13 = 4.615384615 hours = 4 hours 36.9 minutes, 

                   
Edwin

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