Variation on Combined Work

Hi Vibhuti,

It sounds to me like you're saying:

A large pipe can fill 1/2 a pool in 4 hours.

A small pipe can fill 1/2 the same pool in 9 hours.

Together, the pipes can fill the pool in 12 hours.

But this can't be right, because then the answers are trivial:
The large pipe can fill the pool in 8 hours, and the small one
can fill it in 18.

Or are you saying:

If you run a large pipe for 4 hours, and run a small pipe
for 9 hours, you can fill 1/2 a pool.

If you run both pipes together for 12 hours, you can
fill the whole pool.

Is that correct?

If so, let's say that the pool holds G gallons, that the large pipe
contributes R gallons per hour, and the small pipe contributes r
gallons per hour. Then

4R + 9r = G/2 (First condition)

12(R + r) = G (Second condition)

Doubling the first equation gives us

8R + 18r = G

12(R + r) = G

Two things that are equal to the same thing are equal to each
other, so

8R + 18r = 12(R + r)

So you can use this to find out the ratio of the rates for the
two pipes,

R = kr

Then you can substitute that back into the equation

12(kr + r) = G

to find out how long the smaller pipe needs to fill the whole
pool; which will tell you how long it takes the larger pipe to
fill the whole pool.

Can you take it from here?