You walk at a pace of 3 miles per hour, and jog at a pace of 6 miles per hour. You want to cover a distance of more than 18 miles in less than hours. Write a system of inequalities to represent the situation. What is one possible combination of the number of hours you walk/ jog to achieve your goal?

Question

You walk at a pace of 3 miles per hour, and jog at a pace of 6 miles per hour. You want to cover a distance of more than 18 miles in less than hours. Write a system of inequalities to represent the situation. What is one possible combination of the number of hours you walk/ jog to achieve your goal?

Answer 1

proofread how many hours?

Answer 2

well, start with

time = distance/speed

Answer 3

To represent the situation, we can use the variables w and j to represent the number of hours spent walking and jogging, respectively.

The first inequality represents the distance covered by walking, which is 3 miles per hour multiplied by the number of hours spent walking, greater than or equal to 18 miles:
3w ≥ 18

The second inequality represents the distance covered by jogging, which is 6 miles per hour multiplied by the number of hours spent jogging, less than 18 miles:
6j < 18

To find a possible combination of the number of hours you walk/jog to achieve your goal, we need to solve this system of inequalities.

Let's solve it using substitution method:
From the first inequality, we can determine that w ≥ 6 (by dividing both sides by 3).
From the second inequality, we can determine that j < 3 (by dividing both sides by 6).

One possible combination could be:
w = 7 hours (you walk for 7 hours)
j = 2 hours (you jog for 2 hours)

Let's substitute these values into the inequalities to check:
3(7) ≥ 18 (21 ≥ 18), which is true
6(2) < 18 (12 < 18), which is also true

Therefore, walking for 7 hours and jogging for 2 hours would be one possible combination to cover a distance of over 18 miles in less than 3 hours.