see fast

[skillszone]

Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to
fill the tank

[Dsg]

If V = the volume of tank:

Pump A is filling at a rate of 3V per hour

Pump B at 2V per hour

Pump C is emptying at a rate of 1.5V per hour

The net of all 3 working together is 3V+2V-1.5V=3.5V per hour.

So the tank will be full in 60/3.5 = 17mins (just over).

[crofter]

Arguing non-algebraically (without the symbol V)

Let the pumps work for 2 full hours (120 minutes). In this time, Pump A can fill 6 tanks, Pump can fill 4 tanks and Pump C can empty 3 tanks. Taken together a total of 7 tanks can be filled.

Hence, 7 tanks in 120 minutes.

Therefore, ! tank in 120/7 minutes ( = 17 and 1/7mins)

Not everyone is as skilled in algebra as Dsg. Well done