One pipe can fill a tank in 60 minutes and another pipe can fill it in 50 minutes .If these two pipes are open and a third pipe is draining water from the tank ,it take 35 minutes to fill the tank .How long will it take the third pipe alone to empty the tank?
how much of the tank's volume is filled/drained each minute?
1/60 + 1/50 - 1/x = 1/35
1/x = 17/2100
So, it will take 2100/17 = 123.5 minutes
To solve this problem, let's consider the rates at which each pipe fills or empties the tank.
Pipe 1 can fill the tank in 60 minutes, which means its filling rate is 1/60 of the tank per minute.
Pipe 2 can fill the tank in 50 minutes, so its filling rate is 1/50 of the tank per minute.
The combined filling rate of pipe 1 and pipe 2 is the sum of their individual rates, which is 1/60 + 1/50 = 11/300 of the tank per minute.
If the two pipes are open and a third pipe is draining water from the tank, it takes 35 minutes to fill the tank. This means that the combined filling rate of pipe 1, pipe 2, and the third pipe is 1/35 of the tank per minute.
To find the rate at which the third pipe drains water from the tank, we subtract the combined filling rate of pipe 1 and pipe 2 from the combined filling and draining rate. So, the draining rate of the third pipe is:
1/35 - 11/300 = 60/1050 - 11/300 = -11/300 + 60/1050 = -33/700
The negative sign indicates that the third pipe is draining water from the tank. The absolute value of -33/700 is 33/700, which represents the rate at which the third pipe empties the tank.
To find out how long it will take the third pipe alone to empty the tank, we invert its rate and multiply it by the tank capacity:
Time = Tank Capacity / Rate = 1 / (33/700) = 700 / 33 = 21.21 minutes (rounded to two decimal places)
Therefore, it will take approximately 21.21 minutes for the third pipe alone to empty the tank.