Filling a tank A water tank has an inlet pipe and a drain pi

Filling a tank. A water tank has an inlet pipe and a drain
pipe. A full tank can be emptied in 30 minutes if the drain
is opened and an empty tank can be filled in 45 minutes
with the inlet pipe opened. If both pipes are accidentally
opened when the tank is full, then how long will it take to
empty the tank?

Solution

Filling a tank. A water tank has an inlet pipe and a drain
pipe. A full tank can be emptied in 30 minutes if the drain
is opened and an empty tank can be filled in 45 minutes
with the inlet pipe opened. If both pipes are accidentally
opened when the tank is full, then how long will it take to
empty the tank?
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Drain Pipe DATA:
time = 30 min/job ; rate = 1/30 job/min
-----------------------
Fill Pipe DATA:
time = 45 min/job ; rate = 1/45 job/min
-------------------------
Together DATA:
time = x min/job ; rate = 1/x job/min
--------------------------------------------
Equation:
fill rate - drain rate = together rate
1/30 - 1/45 = 1/x
45x - 30x = 30*45
15x = 30*45
x = 2*45
x = 90 minutes (time for both pipes together to fill the tank)