Question

Solve the problem.

Step 1

Let M, J, B = fences per hour for Mike, Joe, Bill respectively.

Equations:

- 4 (M + J) + 2 B = 1 (i)
- 2 (M + J) + 5 B = 1 (ii)
- 6 M + 2 J + 1 B = 1 (iii)

Let's Franklin be the person can work as fast as Mike and Joe together.

So, F = M + J

From the first equation, we get

4 F + 2 B = 1 fence

From the second equation, we get

2 F + 5 B = 1 or

4 F + 10 B = 2

Subtracting equation (i) from equation (ii) , we get

8 B = 1

B = 1/8

So, Bill paints the fence in 8 hours.

Step 2

From equation (iii) we have

6 M + 2 J + 1/8 = 1

6 M + 2 J = 7/8 (iv)

From equation (ii) we have

2 M + 2 J = 3/8 (v)

Subtracting equation (iv) f...

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