Answer:
Option 1 is correct. i.e 2 hours walking; 12 hours running
Step-by-step explanation:
We are given the equations
3w + 6r ≥ 36
3w + 6r ≤ 90
We will check which of the option satisfy the above equations.
1) 2 hours walking; 12 hours running
w = 2 and r =12
3w + 6r ≥ 36
3(2) + 6(12) ≥ 36
6+72 ≥ 36
78 ≥ 36
3w + 6r ≤ 90
3(2) + 6(12) ≤ 90
6+72 ≤ 90
78 ≤ 90
Both equations are satisfied. Option 1 is correct.
2) 4 hours walking; 3 hours running
w = 4 and r =3
3w + 6r ≥ 36
3(4) + 6(3) ≥ 36
12+18 ≥ 36
30 ≥ 36 (this equation doesn't hold as 30 < 36 and not < or equal to 36)
3w + 6r ≤ 90
3(4) + 6(3) ≤ 90
12+18 ≤ 90
30 ≤ 90
So, Option 2 is incorrect.
3) 9 hours running 12 hours walking
w = 9 and r =12
3w + 6r ≥ 36
3(9) + 6(12) ≥ 36
27+72 ≥ 36
99 ≥ 36
3w + 6r ≤ 90
3(9) + 6(12) ≤ 90
27+72 ≤ 90
99 ≤ 90 (this equation doesn't hold because 99 is greater than 90 and not less than 90)
Option 3 is incorrect.
4) 12 hours walking; 10 hours running
w = 12 and r =120
3w + 6r ≥ 36
3(12) + 6(10) ≥ 36
36+60 ≥ 36
96 ≥ 36
3w + 6r ≤ 90
3(12) + 6(10) ≤ 90
36+60 ≤ 90
99 ≤ 90 (this equation doesn't hold because 96 is greater than 90 and not less than 90)
Option 4 is incorrect.
