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 5 hours.
Write a system of inequalities to represent the situation. What is one possible combination of the number of hours you can walk/ jog to achieve your goal?
w + j > 18
w/3 + j/6 < 5 ... 2w + j < 30
walk 1 hr, jog 3 hr
Let's represent the number of hours walking as "w" and the number of hours jogging as "j".
Given:
- Walking pace: 3 miles per hour
- Jogging pace: 6 miles per hour
- Target distance: more than 18 miles
- Time constraint: less than 5 hours
System of inequalities:
1. Total distance covered: 3w + 6j > 18
2. Total time spent: w + j < 5
To find one possible combination of the number of hours you can walk/jog to achieve your goal, we can substitute different values for either "w" or "j" and solve the system of equations.
Let's assume:
w = 2 hours (walking for 2 hours)
Substituting w = 2 into the second equation:
2 + j < 5
j < 3
So, if you walk for 2 hours, you can jog for less than 3 hours to cover a distance of more than 18 miles in less than 5 hours.
To represent the situation, we can set up the following system of inequalities:
Let x represent the number of hours you walk, and y represent the number of hours you jog.
1. Walking speed: x * 3 > 18
This inequality states that the distance covered by walking, which is the number of hours walked (x) multiplied by the walking pace (3 miles per hour), should be greater than 18 miles.
2. Jogging speed: y * 6 > 18
This inequality states that the distance covered by jogging, which is the number of hours jogged (y) multiplied by the jogging pace (6 miles per hour), should be greater than 18 miles.
3. Time constraint: x + y < 5
This inequality states that the total time spent walking and jogging, which is the sum of the number of hours walked (x) and the number of hours jogged (y), should be less than 5 hours.
One possible combination of the number of hours you can walk/jog to achieve your goal can be:
x = 3 (hours of walking)
y = 1 (hour of jogging)
Substituting these values into the inequalities:
1. Walking speed: 3 * 3 = 9 (miles)
As 9 miles is greater than 18 miles, this inequality is satisfied.
2. Jogging speed: 1 * 6 = 6 (miles)
As 6 miles is greater than 18 miles, this inequality is also satisfied.
3. Time constraint: 3 + 1 = 4 (hours)
As 4 hours is less than 5 hours, this inequality is satisfied.
Therefore, walking for 3 hours and jogging for 1 hour is one possible combination that meets the given conditions.