Jeff takes 5 hours longer to build a fence than it takes Bill. When they work together, it takes them 6 hours. How long would it take Bill to do the job alone?
A) 9 hours
B) 11 hours
C) 12 hours
D) 10 hours

Question

Quizplus · Accepted Answer

When Jeff and Bill work together, their combined work rate is 1/6 of the job per hour (since it takes them 6 hours to complete the job together). Let's denote the time it takes for Bill to build the fence alone as $B$ hours. Therefore, Jeff takes $B + 5$ hours to do the job alone. The work rate of Bill is $1/B$ of the job per hour, and the work rate of Jeff is $1/(B + 5)$ of the job per hour. Adding their rates gives the equation $1/B + 1/(B + 5) = 1/6$. Solving this equation for $B$ gives $B = 10$ hours.

Jeff Takes 5 Hours Longer to Build a Fence Than