Martha can rake the leaves in her yard in 4 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together?
A) $7 \mathrm{hr}$
B) $\frac{28}{3} \mathrm{hr}$
C) $\frac{11}{28} \mathrm{hr}$
D) $\frac{28}{11} \mathrm{hr}$

Question

Quizplus · Accepted Answer

Martha's rate is $1/4$ of the yard per hour, and her brother's rate is $1/7$ of the yard per hour. Together, they can rake $(1/4 + 1/7) = (7/28 + 4/28) = 11/28$ of the yard per hour. To find the time it takes to rake the entire yard, take the reciprocal of their combined rate, which is $\frac{28}{11}$ hours.

Martha Can Rake the Leaves in Her Yard in 4 7hr7 \mathrm{hr}7hr

Martha Can Rake the Leaves in Her Yard in 4 $7 \mathrm{hr}$