Solve using the Gaussian Elimination and show all work.
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 would it take each man to paint the entire fence by himself?
Lets denote by x the fraction of the fence each man paints in a single hour.
For Mike it is xm, For ...
The solution helps the student make the connection between the initial wording of the problem to the final equations needed to solve the problem.