SOLUTION: 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

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Question 329130: 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 i t take to empty the tank?
Found 2 solutions by nerdybill, vksarvepalli:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
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 i t take to empty the tank?
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Let t = time it takes to empty tank
then
1 - t(1/30) + t(1/45) = 0
1 - t/30 + t/45 = 0
multiplying both sides by (30)(45):
1350 - 45t + 30t = 0
1350 - 15t = 0
1350 = 15t
90 minutes = t

Answer by vksarvepalli(154) (Show Source):
You can put this solution on YOUR website!
Let the volume of the tank be V litres
Now, A full tank can be emptied in 30 minutes if the drain is opened
so in one minute V/30 litres will be drained.
and an empty tank can be filled in 45 minutes with the inlet pipe opened
so in one minute V/45 litres will be filled into the tank.
now both pipes are opened when the tank is full.
when both pipes are opened per minute V/45 litres enter and V/30 litres exit the tank.
so in net V/30 - V/45 litres exit per minute
that is V/90 litres per minute are drained from the tank when both pipes are opened .
so for the whole tank that is V litres to be emptied,
the time required will be
= V/(V/90)
= 90 mins
so when the both pipes are opened the time taken to empty the full tank is 90 minutes.
Answer: 90 minutes