a water tank can be filled in 10 hours by an inlet pipe and emptied in 15 hours by an outlet pipe. how long will it take to fill the tank if both pipes ate left

Question

It's an story problem

 

Answer 1

Tank filled in 10 hours   ==>   in 1 hour 1/10 of the tank is filled

Tank emptied in 15 hours ==> in 1 hour 1/15 of the tank is emptied  

 

So every hour the amount in the tank goes up by 1/10 and goes down by 1/15, so the net change is

1/10 - 1/15 per hour

 

So in X hours the net change will be X * ( 1/10 - 1/15 )

 

The tank will be full when

 

X * ( 1/10 - 1/15) = 1

X * ( 3/30 - 2/30) = 1

X * ( 1/30 ) = 1

X = 30 hours 

 

Check:  In 30 hours the tank is filled 30/10 = 3 times and emptied 30/15 = 2 times so the net change is 1 complete filling