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 pip

Question 258175: 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?
Found 2 solutions by stanbon, palanisamy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
-------------------------------------------------
Filling tank DATA:
rate = 1/30 job/min
------
Emptying tank DATA:
rate = 1/45 job/min
---------------------
Together DATA:
rate = 1/x job/min
==========================
Equation:
rate - rate = together rate
1/30 - 1/45 = 1/x
---
(45-30)/(30*45) = 1/x
15x = 30*45
x = 90 minutes (amt. of time needed to fill the tank)
==================
Cheers,
Stan H.

Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Given, a full tank can be emptied in 30 minutes if the drain is opened.
So in 1 minute 1/30 of the tank can be emptied.
And an empty tank can be filled in 45 minutes with the inlet pipe opened.
So in 1 minute 1/45 of the tank can be filled.
If both are opened, in one minute, [(1/30)-(1/45)]of the tank can be emptied.
Time taken to empty the full tank = 1/[(1/30)-(1/45)]
= 1/[(45-30)/45*30]
= 45*30/15
= 3*30
= 90 minutes
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