Expert: Sherry Wallin - 11/15/2009

Question
Pipe A leads into a tank, and Pipe B drains the tank. Pipe A can fill the entire tank in 10 minutes. Pipe B can drain the entire tank in 8 minutes. At a certain point in time, the valves leading to both pipes are shut and the tank is  full. If both valves are opened simultaneously, how long will it take for the pipe to drain?


Answer
Hi David~
    This is a work rate type problem. You know in a work problem that the rate is 1 over the time so if it takes 3 hours to do one job then you are working at a rate of 1/3 job per hour or 1job/3hr, one job every three hours. Here the work (one job) is either filling or draining the tank. When your tank is full one rate is the rate the tank is draining which is 1/8 tank per minute but at the same time it is filling the tank at a rate of 1/10 tank per min. Since we are looking for when the tank is emptied and 1/8 is larger than 1/10 we have the following rational equation to solve:
[(1/8)t - (1/10)t] = 1 which can be interpreted as one-eighth of the job per minute minus one-tenth of the job per minute = 1 job (tank drain). Multiply all by LCM = 40 getting 5t - 4t = 40 or t = 40 minutes to complete one job. i.e., after 40 min the tank will be drained.

Math Prof