A contractor finds that it takes Julie 11 hours to construct a wall of a certain size. It takes Leann 8 hours to construct the same wall. How long would it take if they worked together?

A) $\frac{19}{88}$ hours

B) 19 hours

C) 1 hour

D) $4 \frac{12}{19}$ hours

Question

A contractor finds that it takes Julie 11 hours to construct a wall of a certain size. It takes Leann 8 hours to construct the same wall. How long would it take if they worked together?

A) $\frac{19}{88}$ hours

B) 19 hours

C) 1 hour

D) $4 \frac{12}{19}$ hours

Quizplus · Accepted Answer

Julie's work rate is $1/11$ of the wall per hour, and Leann's is $1/8$ of the wall per hour. Together, they work at a rate of $(1/11 + 1/8)$ walls per hour, which simplifies to $19/88$ walls per hour. To find the time taken to build one wall, take the reciprocal of their combined rate, which gives $88/19$ hours, or $4 \frac{12}{19}$ hours.

A Contractor Finds That It Takes Julie 11 Hours to Construct