MATH SOLVE

5 months ago

Q:
# 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 β₯ 36 3w + 6r β€ 90 Which combination of hours can Keitaro walk and run in a month to reach his goal? 2 hours walking; 12 hours running 4 hours walking; 3 hours running 9 hours walking; 12 hours running 12 hours walking; 10 hours running

Accepted Solution

A:

Answer:A. 2 hours walking; 12 hours runningStep-by-step explanation:The combination of hours walking and running has to respect both these inequalities:[tex]3w + 6r \geq 36[/tex][tex]3w + 6r \leq 90[/tex]A. 2 hours walking; 12 hours running3w + 6r = 3*2 + 6*12 = 6+72 = 78.Ok, it is larger than 35 and smaller than 91.B. 4 hours walking; 3 hours running3w + 6r = 3*4 + 6*3 = 12 + 18 = 30.Invalid. Lesser than 36.C. 9 hours walking; 12 hours running3w + 6r = 3*9 + 6*12 = 27 + 72 = 99Larger than 90. InvalidD. 12 hours walking; 10 hours running3w + 6r = 3*12 + 6*10 = 96Larger than 90. Invalid