One painter can paint a fence in 8 hours. A second painter works twice as fast as the first. Working together, how long will it take them…

The first painter paints $\frac{1}{8}$ of the fence per hour. The second works twice as fast, so paints $\frac{2}{8}=\frac{1}{4}$ per hour. Together they paint $\frac{1}{8}+\frac{1}{4}=\frac{3}{8}$ of the fence per hour, so the time is $\frac{8}{3}\approx2.67$ hours, choice G. The answer must be less than the faster painter's solo time of $4$ hours, which rules out choices H and J. Choice F ($2.4$) comes from using the wrong combined rate, such as $\frac{5}{12}$. Time is the reciprocal of the combined rate.