Question

Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal. 3w + 6r ≥ 36 3w + 6r ≤ 90 Which combination of hours can Keitaro walk and run in a month to reach his goal?

Answer 1

2 hours walking and 12 hours running

Explanation:

The choice to this question are

• 2 hours walking; 12 hours running
• 4 hours walking; 3 hours running
• 9 hours walking; 12 hours running
• 12 hours walking; 10 hours running

The given inequalities are

`3w+6r\geq 36`

`3w+6r\leq 90`

Where
`w` is walk and
`r` is run.

First, we need to graph this system. The image attached shows both inequalities and the area of solution, where
`x=w` and
`y=r`.

In other words, any point in side the intesection of shaded areas is part of the solution to this problem.

So, 2 hours walking and 12 hours running is inside the area of solution, because represents point (2,12).