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 ≥ 363w + 6r ≤ 90Which combination of hours can Keitaro walk and run in a month to reach his goal?A. 2 hours walking; 12 hours runningB. 4 hours walking; 3 hours runningC. 9 hours walking; 12 hours runningD. 12 hours walking; 10 hours running

Answer 1

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

Answer 2

Answer:

A. 2 hours walking; 12 hours running

Step-by-step explanation:

The combination of hours walking and running has to respect both these inequalities:

$3w + 6r \geq 36$

$3w + 6r \leq 90$

A. 2 hours walking; 12 hours running

3w + 6r = 3*2 + 6*12 = 6+72 = 78.

Ok, it is larger than 35 and smaller than 91.

B. 4 hours walking; 3 hours running

3w + 6r = 3*4 + 6*3 = 12 + 18 = 30.

Invalid. Lesser than 36.

C. 9 hours walking; 12 hours running

3w + 6r = 3*9 + 6*12 = 27 + 72 = 99

Larger than 90. Invalid

D. 12 hours walking; 10 hours running

3w + 6r = 3*12 + 6*10 = 96

Larger than 90. Invalid