Question

Original problem statement:

Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it takes 2 hours, and with only valves B and C open it takes 3 hours. How long will it take to fill the tank with only valves A and B open?

Analysis:

Three valves with flow rates (vol / time) of A, B, C.
Thus, in a time t, the A valve delivers a volume of At.

Let the total volume of the tank equal 1 in our units.
In each case below, we start at t = 0 with the tank empty.

Answer 1

With all 3 valves open, the tank is filled in time t = 1, so we have:
A + B + C = 1

With just A and B open, the tank is filled at time t = 2, so we have:
2A + 2B = 1

And with valves B and C open, the tank is filled at time t = 3.
3B + 3C = 1

My solution is:

A = 2/3
B = -1/6
C = 1/2

Answer 2

@lgbasallote
original problem is here:
http://openstudy.com/users/azntiger627#/updates/50171993e4b04dfc808b5196
Can you please explain your answer more, in particular use of the reciprocal.

Answer 3

Thanks.

Answer 4

Having trouble with links. Your analysis is above. Original problem is
http://openstudy.com/users/azntiger627#/updates/50170e92e4b04dfc808b485d

Answer 5

Guess I forgot to do the last part:
At + Bt = 1
2/3 - 1/6 t = 1/2 t = 1
t = 2

Answer 6

I see a problem with this.