Pipe A can fill a tank in 6 hours, and pipe B can fill it in 2 hours less time than it take drain pipe C to empty the tank. With all three pipes open it takes 3 hours 20 minutes to fill the tank. How long would it take pipe C to empty it
Make this chart:
Number of Time to Rate in
tanks filled fill tanks/hours
Pipe A
Pipe B
Drain C
All three
The number of tanks filled is 1 for each of those except Drain C, and
we put -1 for the number of tanks it filled. We can fill in the times
for C and All three from the problem, and we get this:
Number of Time to Rate in
tanks filled fill tanks/hours
Pipe A 1 6
Pipe B 1
Drain C -1
All three 1 3 1/3
Let the time for C to drain be x. Then B's time to fill is x-2.
Fill those in:
Number of Time to Rate in
tanks filled fill tanks/hours
Pipe A 1 6
Pipe B 1 x-2
Drain C -1 x
All three 1 3 1/3
Fill in the rates in tanks/hour by dividing the number of
tanks filled by the number of hours:
Number of Time to Rate in
tanks filled fill tanks/hours
Pipe A 1 6 1/6
Pipe B 1 x-2 1/(x-2)
Drain C -1 x -1/x
All three 1 3 1/3
First we simplify the last term:
The LCD is 30x(x-2) so multiply through by that:
,
Discard the negative time.
It would take drain C 5 hours to empty the tank.
Edwin