Let w = number of hours it would take to paint the mural one woman.
Let g = number of hours it would take to paint the mural one girl.

Then one woman paints  of the mural per hour. 8 women paint  of the mural per one hour.
One girl paints  of the mural per hour. 12 girls paint  of the mural per one hour.

In this way you get the system of two equations 

 +  = ,   (1)

 +  = .    (2)

for two unknowns w and g. To solve it, multiply equation (1) by 2 (both sides) and equation (2) by -3, then add.
Thus you exclude the variable g and get an equation for the variable w only:

 = ,   or

 =  = .

It gives w = 140. Hence, it takes 140 hours for 1 woman to paint the mural.

Now please complete the solution yourself.