Problem Solving

A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am

B)10:45am

C)12:00pm

D)12:30pm

E)1:30pm

OA [spoiler]c

source -Veritas prep[/spoiler]

guerrero wrote:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am

B)10:45am

C)12:00pm

D)12:30pm

E)1:30pm

Let the tank = 30 liters.

Rate for the inlet pipe = w/t = 30/5 = 6 liters per hour.
Rate for the outlet pipe = w/t = 30/15 = 2 liters per hour.
When the inlet pipe and the outlet pipe work together, the inlet pipe pumps IN 6 liters per hour, while the outlet pipe pumps OUT 2 liters per hour.
Thus, the NET rate for the 2 pipes working together = 6-2 = 4 liters per hour.

To fill the tank in 6 hours, the required average rate = w/t = 30/6 = 5 liters per hour.
The required average rate (5 liters per hour) is HALFWAY between the rate for the inlet pipe alone (6 liters per hour) and the rate for the 2 pipes working together (4 liters per hour).
Implication:
For 1/2 the time (3 hours) the inlet pipe must work alone.
For 1/2 of the time (the remaining 3 hours) the 2 pipes must work together.
Since the inlet pipe works alone for 3 hours, the outlet pipe is turned on 3 hours after the start time:
9:30am + 3 hours = 12:30pm.

The correct answer is D.