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.
$3w + 6r \geq 36$
$3w + 6r \leq 90$
which combination of hours can keitaro walk and run in a month to reach his goal?
\\(\circ\\) 2 hours walking; 12 hours running
\\(\circ\\) 4 hours walking; 3 hours running
\\(\circ\\) 9 hours walking; 12 hours running
\\(\circ\\) 12 hours walking; 10 hours running

Explanation:

Step1: Check Option 1 (2w,12r)

Calculate total miles: $3(2) + 6(12) = 6 + 72 = 78$. Check inequalities: $36 \leq 78 \leq 90$? Yes.

Step2: Check Option 2 (4w,3r)

Total miles: $3(4) + 6(3) = 12 + 18 = 30$. $30 \geq 36$? No.

Step3: Check Option 3 (9w,12r)

Total miles: $3(9) + 6(12) = 27 + 72 = 99$. $99 \leq 90$? No.

Step4: Check Option 4 (12w,10r)

Total miles: $3(12) + 6(10) = 36 + 60 = 96$. $96 \leq 90$? No.

Answer:

A. 2 hours walking; 12 hours running