a new crew of painters takes two times as long to paint a small apartment as an experienced crew. together…

Answer:

12

Explanation:

Step1: Define variables

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.

Step2: Calculate work - rates

The work - rate of the experienced crew is $\frac{1}{x}$ of the apartment per hour, and the work - rate of the new crew is $\frac{1}{2x}$ of the apartment per hour.

Step3: Set up the equation

Since together they can paint the apartment in 4 hours, their combined work - rate is $\frac{1}{4}$ of the apartment per hour. So, $\frac{1}{x}+\frac{1}{2x}=\frac{1}{4}$.

Step4: Combine fractions on the left - hand side

$\frac{2 + 1}{2x}=\frac{1}{4}$, which simplifies to $\frac{3}{2x}=\frac{1}{4}$.

Step5: Cross - multiply

$2x\times1=3\times4$.

Step6: Solve for $x$

$2x = 12$, so $x = 6$.

Step7: Find the time for the new crew

Since it takes the new crew $2x$ hours, and $x = 6$, then the new crew takes $2\times6=12$ hours.