A homeowner estimates that it will take her 8 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?
A) $3 \frac { 1 } { 13 } \text { days }$
B) $1 \frac { 1 } { 13 } \text { days }$
C) $2 \frac { 1 } { 13 } \text { days }$
D) $$3 \frac { 3 } { 13 }$$
days
E) $3 \frac { 1 } { 14 } \text { days }$

Question

Quizplus · Accepted Answer

The homeowner can roof the house at a rate of $1/8$ of the house per day, and the roofer can do $1/5$ of the house per day. Together, they can do $(1/8 + 1/5)$ of the house per day, which simplifies to $13/40$ of the house per day. To complete the house, it would take $1 / (13/40) = 40/13$ days, which is $3 \frac { 1 } { 13 } \text { days }$.

A Homeowner Estimates That It Will Take Her 8 Days 3113 days 3 \frac { 1 } { 13 } \text { days }3131​ days

A Homeowner Estimates That It Will Take Her 8 Days $3 \frac { 1 } { 13 } \text { days }$