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 wi

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Question 201658This question is from textbook
: 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? This question is from textbook

Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

By itself, the drain can empty of the tank in 1 minute. By itself, the inlet can fill of the tank in 1 minute.

Since filling takes longer than emptying, the net effect is that the tank will empty itself, so with both valves open,



of the tank will empty in one minute, and it will then take



minutes for the tank to empty. You get to do the arithmetic. Hint: LCD = 90.

John

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
--------------------
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)
===========================================
Cheers,
Stan H.