If you enter Interstate 40 at mile marker 23 in Sayre, Oklahoma, how far would you need to travel to reach mile marker 125 in El Reno, Oklahoma? After reaching El Reno, you might worry that your vehicle is running low on fuel. You know that your vehicle can travel 32 miles per gallon (miles/gallon).
· Write an inequality that shows the mile markers (m) that you can reach from El Reno, traveling in either direction, when g is the amount of fuel, in gallons, in your vehicle. Explain what this means.
To determine the inequality that shows the mile markers you can reach from El Reno, traveling in either direction, we need to consider the amount of fuel (g) in your vehicle and the fuel efficiency, which is given as 32 miles per gallon (miles/gallon).
Let's assume the initial amount of fuel in your vehicle is g gallons. We know that you can travel 32 miles for every gallon of fuel. Therefore, by multiplying the amount of fuel (g) by the fuel efficiency (32 miles/gallon), we can determine the total distance you can travel.
However, since we're interested in the mile markers you can reach from El Reno, we need to consider two scenarios:
1. Traveling in the positive direction (eastbound): In this case, you're moving away from Sayre, Oklahoma. The inequality to represent the mile markers you can reach from El Reno in the positive direction is:
m - 125 ≤ g * 32
This means that the difference between the mile marker (m) and 125 (mile marker in El Reno) should be less than or equal to the total distance you can travel (g * 32) based on the amount of fuel in your vehicle.
2. Traveling in the negative direction (westbound): In this case, you're moving towards Sayre, Oklahoma. The inequality to represent the mile markers you can reach from El Reno in the negative direction is:
125 - m ≤ g * 32
This means that the difference between 125 (mile marker in El Reno) and the mile marker (m) should be less than or equal to the total distance you can travel (g * 32) based on the amount of fuel in your vehicle.
By setting up these inequalities, you can determine the range of mile markers you can reach from El Reno in either direction based on your vehicle's fuel capacity.