Solve the Problem by Writing and Solving a Suitable System $16 \mathrm{hr}$

Solve the problem by writing and solving a suitable system of equations.
-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 $16 \mathrm{hr}$ , Joe $8 \mathrm{hr}$ , Bill $8 \mathrm{hr}$
B) Mike 8 hr, Joe 8 hr, Bill $16 \mathrm{hr}$
C) Mike 8 hr, Joe 16 hr, Bill 8 hr
D) Mike 12 hr, Joe 10 hr, Bill $10 \mathrm{hr}$