Use the following law which makes this so much easier.

Hacker's Rule of Combine WorkIf a man does a job in A hours and a woman does a job in B hours then the combined work is:

AB/(A+B)

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,

(LS)/(L+S)=4

We also know that,

L+6=S

Substitute that into the equation,

[L(L+6)]/[L+(L+6)]=4

Thus,

(L^2+6L)/(2L+6)=4

Multiply by denominator,

L^2+6L=8L+24

Solve quadradic for positive root.

L=6

That means,

S=12.

This is Mine 48th Post!!!