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 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

Answer 2

The combination of hours Keitaro can walk and run in a month to reach his goal is 2 hours walking; 12 hours running

3w + 6r ≥ 36. (1)

3w + 6r ≤ 90. (2)

substitute each option into the equation

A. 2 hours walking; 12 hours running

3w + 6r ≥ 36

3(2) + 6(12) ≥ 36

6 + 72 ≥ 36

78 ≥ 36

True

3w + 6r ≤ 90

3(2) + 6(12) ≤ 90

6 + 72 ≤ 90

78 ≤ 90

True

B. 4 hours walking; 3 hours running

3w + 6r ≤ 90

3(4) + 6(3) ≤ 90

12 + 18 ≤ 90

30 ≤ 90

True

B. 4 hours walking; 3 hours running

3w + 6r ≥ 36

3(4) + 6(3) ≥ 36

12 + 18 ≥ 36

30 ≥ 36

False

C. 9 hours walking; 12 hours running

3w + 6r ≥ 36

3(9) + 6(12) ≥ 36

27 + 72 ≥ 36

99 ≥ 36

True

3w + 6r ≤ 90

3(9) + 6(12) ≤ 90

27 + 72 ≤ 90

99 ≤ 90

False

D. 12 hours walking; 10 hours running

3w + 6r ≥ 36

3(12) + 6(10) ≥ 36

36 + 60 ≥ 36

96 ≥ 36

True

3w + 6r ≤ 90

3(12) + 6(10) ≤ 90

36 + 60 ≤ 90

96 ≤ 90

False.

Therefore, the combination of hours Keitaro can walk and run in a month to reach his goal is 2 hours walking; 12 hours running

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