a new crew of painters can paint a small apar...
a new crew of painters can paint a small apartment in 12 hours. an experienced crew can paint the small apartment in 6 hours. how many hours does it take to paint the apartment when the two crews work together? it takes ______ hours to paint the apartment when the two crews work together. the solution is
Answer
# Explanation:
## Step1: Calculate work - rate of each crew
The new crew can paint the apartment in 12 hours, so their work - rate is $\frac{1}{12}$ of the apartment per hour. The experienced crew can paint the apartment in 6 hours, so their work - rate is $\frac{1}{6}$ of the apartment per hour.
## Step2: Calculate combined work - rate
The combined work - rate of the two crews is $\frac{1}{12}+\frac{1}{6}=\frac{1 + 2}{12}=\frac{3}{12}=\frac{1}{4}$ of the apartment per hour.
## Step3: Calculate time taken when working together
Let $t$ be the time taken when they work together. Since work = rate×time and the work is 1 apartment, we have $\frac{1}{4}t = 1$. Solving for $t$, we get $t = 4$ hours.
# Answer:
4