A new crew of painters takes two times as long to paint a small apartment as an experienced crew. Together, both crews can paint the apartment in 4 hours. How many hours does it take the new crew to paint the apartment?
It takes blank hours for the new crew to paint the apartment.
The solution is
Let x be the number of hours it takes the experienced crew to paint the apartment. Then it takes 2x hours for the new crew to paint the apartment.
The rate at which the experienced crew paints is 1/x and the rate at which the new crew paints is 1/2x.
Together, the rate at which both crews paint is 1/x + 1/2x = 1/4.
Multiplying through by 4x, we get:
4 + 2 = x
x = 6
Therefore, it takes the new crew 2*6 = 12 hours to paint the apartment.