math

v ₁=1/15
v ₂=1/10
v _ges=v ₁+v ₂=1/15+1/10=1/6
t=1/v _ges=6

Peter's answer is perfect but for some of you, who are less comfortable with algebra you may like to look at it this way.

Firstly, no matter how many windows there are in the building, the answer will be the same.
Just to make it easier I'm going to say there are 150 windows in the buiding

worker one takes 15 hours to wash them all so he must be washing 150/15 = 10 windows per hour
worker two takes 10 hours to wash them all so he must be washing 150/10 = 15 windows per hour

Together they will wash 10+15 = 25 windows per hour

150 windows at 25 windows per hour is 6 hours.