2 pipes can fill in 6 h and 12 h. the other pipe can empty the tank in 24h. How long would it take to fill the tank with all 3 pipes open?

Question

I have been stuck on this problem for awhile. Someone please help. I am not sure what my variable is.

Answer 1

The variable is Time (how long would it take to fill the tank) 

 

Pipe 1 can fill in 6 h  ==>  in 1 hr pipe 1 can fill 1/6 of tank

Pipe 2 can fill in 12 h  ==> in 1 hr pipe 2 can fill 1/12 of tank

Pipe 3 can empty in 24 h  ==>  in 1 hr pipe 3 can empty 1/24 of tank 

 

In T hours pipes 1 and 2 will fill the tank by T*(1/6 + 1/12)

and pipe 3 will empty the tank by T*(1/24)  

 

The tank will be full when 

T*(1/6 + 1/12 - 1/24) = 1 

 

Note the minus sign to indicate pipe 3 is emptying the tank 

 

Multiply thru by 24 to clear fractions 

 

4*T + 2*T - T = 24

5*T = 24

T = 24/5 = 4.8 h = 4 hours 48 minutes 

 

Check:  In 4.8 h pipe 1 will fill 4.8/6 = 0.8 of the tank

            In 4.8 h pipe 2 will fill 4.8/12 = 0.4 of the tank

            In 4.8 h pipe 3 will empty 4.8/24 = 0.2 of the tank 

            The net change in the tank in 4.8 h is 0.8 + 0.4 - 0.2 = 1.0 complete filling