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.
To solve this problem, we can use the formula for combined work:
1/t = 1/t1 + 1/t2
where t is the time it takes to paint the apartment when the two crews work together, t1 is the time it takes for the new crew to paint the apartment, and t2 is the time it takes for the experienced crew to paint the apartment.
Plugging in the given values:
1/t = 1/12 + 1/6
To add the fractions on the right side of the equation, we need to find a common denominator. The least common multiple of 12 and 6 is 12. Rewriting the equation with the common denominator:
1/t = 1/12 + 2/12
1/t = 3/12
To simplify the fraction on the right side, we can divide both the numerator and denominator by 3:
1/t = 1/4
Now we can see that t = 4.
Therefore, it takes 4 hours for the two crews to paint the apartment together.