Filling a 1000 cubic foot water storage tank

Question

Good day! How can I resolve this?

To fill a 1000 cubic foot water storage tank, three $A, B$ and $C$ inlet pipes can be used. When all three operate at full capacity, the tank can be filled in $10$ hours. When only $A$ and $B$ are used, the time is increased by $20$ hours. Pipes A and C can fill the tank in $12.5$ hours. What is the flow intensity in cubic feet per hour of each of the pipes?

I think this $A+B+C=10,$ $A+B=30$ and $A+C=12.5$ but how can I use the info of $1000?$

Thanks.

Answer 1

Hint:

$A, B, C$ fill the tank in $10$ hours.

In one hour, $A,B,C$ fill up $\frac{1000}{10}=100$ cubic foot of water.

Similarly, $A,B$ fill up $\frac{1000}{30}=\frac{100}{3}$ cubic of water.

and $A,C$ fill up $\frac{1000}{12.5} = 80$ cubic of water.

Let $a,b,c$ be the intensity per hour.

$$a+b+c = 100$$ $$a+b = \frac{100}{3}$$ $$a+c= 80$$

Solve for $a,b,c$.

Answer 2

Hint -

First thing you have to solve this by using 1 hour working.

For example -

A + B + C $= \frac 1{10}$

Similarly other equations.

Then you have to find timings of A, B and C when they working alone.

Intensity of A $= \frac{1000}{\text{Time required by A}}$

Similarly for B and C.