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 6

Question

hours. How many hours does it take the experienced crew to paint the apartment?

It takes blank hours for the experienced crew to paint the apartment.

The solution is

Answer 1

Let \( x \) be the number of hours it takes the experienced crew to paint the apartment.

Since the new crew takes two times as long as the experienced crew, it takes the new crew \( 2x \) hours to paint the apartment.

Now, we can find their rates of working:

• The rate of the experienced crew is \( \frac{1}{x} \) apartments per hour.
• The rate of the new crew is \( \frac{1}{2x} \) apartments per hour.

When both crews work together, their combined rate is: \[ \frac{1}{x} + \frac{1}{2x} = \frac{2}{2x} + \frac{1}{2x} = \frac{3}{2x} \]

According to the problem, together they can paint the apartment in 6 hours. Hence, their combined rate is also \( \frac{1}{6} \) apartments per hour.

Setting the two expressions for the rate equal gives: \[ \frac{3}{2x} = \frac{1}{6} \]

To solve for \( x \), we can cross-multiply: \[ 3 \cdot 6 = 2x \cdot 1 \] \[ 18 = 2x \] \[ x = \frac{18}{2} = 9 \]

Therefore, it takes the experienced crew 9 hours to paint the apartment.

Thus, the solution is: It takes 9 hours for the experienced crew to paint the apartment.