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

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 hours. how many hours does it take the experienced crew to paint the apartment? it takes ______ hours for the experienced crew to paint the apartment. the solution is

Answer

Explanation:

Step1: Define work - rate variables

Let $x$ be the number of hours it takes the experienced crew to paint the apartment. Then the new crew takes $2x$ hours. The work - rate of the experienced crew is $\frac{1}{x}$ (apartment per hour) and the work - rate of the new crew is $\frac{1}{2x}$ (apartment per hour).

Step2: Set up the combined - work equation

Since together they can paint the apartment in 6 hours, their combined work - rate is $\frac{1}{6}$ (apartment per hour). So, $\frac{1}{x}+\frac{1}{2x}=\frac{1}{6}$.

Step3: Combine the left - hand side terms

Find a common denominator for the left - hand side. The common denominator of $x$ and $2x$ is $2x$. So, $\frac{2 + 1}{2x}=\frac{1}{6}$, which simplifies to $\frac{3}{2x}=\frac{1}{6}$.

Step4: Cross - multiply

Cross - multiplying gives $2x\times1=3\times6$.

Step5: Solve for $x$

We have $2x = 18$, then $x = 9$.