Answer: A. 2 hours walking; 12 hours running
Step-by-step explanation:
The system of inequalities that represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal is expressed as
(3w + 6r) ≥ 36w ≤ 90
This shows that he must complete at least 36 miles but not more than 90 miles.
Looking at the possible combination of hours,
A)walking for 2 hours and running for 12 hours would be
3×2 + 6×12 = 6 + 72 = 78 miles
This is actually greater than 36 miles and lesser than 90 miles. Therefore, walking for 2 hours and running for 12 hours combination matches with his goal
Checking the other combinations,
B) 4×3 + 3×6 = 30 miles. It is lesser that 36 miles.
C) 9 × 3 + 12×6 = 99. It is more than 36 miles and more than 90 miles.
D)12×3 + 10×6 = 96 miles