one pipe can fill a tank in 5 hours. another can empty the tank in 8 hours. If both pipes are left open, how long will it take to fill the tank??

Question

please help me answer this anyone.. haha

Answer 1

Let V =the volume of the tank

 

The first pipe fills 1/5 of the tank per hour:  Rate 1 = +V/5 

The second pipe empties 1/8 of the tank per hour:  Rate 2 = -V/8

 

Rate 1 is positive because it's filling the tank.  Rate 2 is negative because it's emptying the tank. We leave each pipe open for a time t, and we want the tank to be full (volume = V) at the end of that time.

 

(Rate 1)*time + (Rate 2)*time = full tank (V)

 

(V/5)t + (-V/8)t = V

 

(1/5 - 1/8)Vt = V   (Factor out V and t)

 

(3/40)t = 1     (Subtract the fractions, divide both sides by V)

 

t = 40/3 = 13 1/3 hours (13 hours 20 minutes)

 

Check:

 

(V/5)(40/3) + (-V/8)(40/3) = (8/3)V - (5/3)V = (3/3)V = V     It fills the tank!