SOLUTION: An inlet pipe can fill up the tank in 6 hours while an outlet pipe can empty the tank in 9 hours. One day, the tank was being filled. When it was 1/3 full, a boy opened the outlet

Question 925607: An inlet pipe can fill up the tank in 6 hours while an outlet pipe can empty the tank in 9 hours. One day, the tank was being filled. When it was 1/3 full, a boy opened the outlet pipe. How long did it take to fill the rest of the tank?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

These problems are like "D=RT" problems, except that the 'distance' is
replaced by 'job to do', The 'job' here is 'one tank'.

An inlet pipe can fill up the tank in 6 hours

So the inlet pipe's filling rate is

while an outlet pipe can empty the tank in 9 hours.

The outlet's emptying rate is considered as a NEGATIVE filling rate.
So the outlet pipe's NEGATIVE filling rate is

One day, the tank was being filled. When it was 1/3 full, a boy opened the outlet pipe.

So the fraction of a job left to do is to fill  of a tankful.

How long did it take to fill the rest of the tank?

Now the filling rate is the sum of the rates of the two pipes:


 and the job is  of a tank.

Just as in "D=RT" problems we use "TIME=DISTANCE/RATE" we use here 
"TIME=JOB/RATE".  The job is  of a tank and the rate is 

So,

 

Edwin

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