Fill Tank in 24 mins Using Pipe A & B

[santa]

There are two pipes, Pipe A and Pipe B. Pipe A filled a tank in for minutes less than B does. If both pipes are open the tank is filled in 24 minutes. Find the time A will take if B is closed

 

[symbolipoint]

The bulk of the analysis for a solution is to fill a chart for Rate, Time, Job, for each of pipe A, pipe B, and pipes A and B together. If anyone knows how to present a chart in the forum, please tell; anyway, I developed this information, using t as time for pipe B to fill the tank:

pipe A: Rate? time=t-4 jobs=1
pipe B: Rate? time=t jobs=1
pipes A and B Together: Rate? time=24 minutes jobs=1

That information further indicates that These rate expressions use:
pipe A: Rate= 1/(t-4)
pipe B: Rate= 1/t
both pipes together: Rate=1/24

I did not finish the solution. Can you continue from there?

 

[HallsofIvy]

Or: add rates. Since the question asks how long it will take A to fill the tank alone, let that be T minutes. Then A's rate is 1/T "tanks per minute". Since A fills the tank in 4 minutes less than B, B fills the tank in 4 minutes longer than A: it fills the tank in T-4 minutes and so its rate is 1/(T-4) "tanks per minute". Together, their rate is 1/T+ 1/(T-4). We are told that the pipes can, together, fill the tank in 24 minutes: their rate together is 1/24 "tanks per minute". Since that is exactly what we calculated before,
1/T+ 1/(T+ 4)=1/24. Solve that equation for T.