Use the following law which makes this so much easier.
Hacker's Rule of Combine Work If a man does a job in A hours and a woman does a job in B hours then the combined work is:
Now, let L be the amount of time for the large tube (in this case man). Let S be the amount of time for the small tube (in this case woman). Then,
We also know that,
Substitute that into the equation,
Multiply by denominator,
Solve quadradic for positive root.
This is Mine 48th Post!!!