Solve the problem.
-Mike, Joe, and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours; or if Mike and Joe work together for 2 hours and Bill Works alone for 5 hours; or if Mike works alone for 6 hours, Joe works alone for 2 hours, and Bill Works alone for 1 hour. How much time does it take for each man working alone to complete the Painting?
A)Mike: 12 hr; Joe: 10 hr; Bill: 10 hr
B)Mike: 8 hr; Joe: 8 hr; Bill: 16 hr
C)Mike: 16 hr; Joe: 8 hr; Bill: 8 hr
D)Mike: 8 hr; Joe: 16 hr; Bill: 8 hr

Question

Quizplus · Accepted Answer

Let the work done by Mike, Joe, and Bill in one hour be $m$, $j$, and $b$ respectively. From the given conditions, we have the following equations:1. $4(m + j) + 2b = 1$ (Mike and Joe for 4 hours plus Bill for 2 hours complete the work)2. $2(m + j) + 5b = 1$ (Mike and Joe for 2 hours plus Bill for 5 hours complete the work)3. $6m + 2j + b = 1$ (Mike for 6 hours, Joe for 2 hours, and Bill for 1 hour complete the work)Solving these equations simultaneously, we find that $m = \frac{1}{8}$, $j = \frac{1}{16}$, and $b = \frac{1}{8}$. Therefore, Mike takes 8 hours, Joe takes 16 hours, and Bill takes 8 hours to complete the painting working alone.

Solve the Problem. -Mike, Joe, and Bill Are Painting a Fence. the Painting