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.
d = 125 - 23 = 102mi.
g = 102mi / 32mi/g = 3.19gal used.
To determine the inequality, let's consider the fuel efficiency of your vehicle and the distance between mile marker 125 in El Reno and the mile marker you're aiming to reach.
The distance between the two mile markers is given by:
Distance = Mile marker of destination - Mile marker of origin
Distance = 125 - 23
Distance = 102 miles
Now, we need to determine the maximum distance you can travel with the amount of fuel in your vehicle. Given that your vehicle travels 32 miles per gallon, the maximum distance you can travel is given by the fuel efficiency multiplied by the amount of fuel, g:
Maximum Distance = g (in gallons) * 32 (miles per gallon)
To represent the mile markers you can reach from El Reno, in either direction, we need to consider two scenarios:
1. When traveling in the positive direction (westbound) from El Reno:
The inequality would be:
125 + Maximum Distance ≥ m
This means that the sum of the mile marker at El Reno (125) and the maximum distance you can travel should be greater than or equal to the mile marker m.
2. When traveling in the negative direction (eastbound) from El Reno:
The inequality would be:
125 - Maximum Distance ≤ m
This means that the difference between the mile marker at El Reno (125) and the maximum distance you can travel should be less than or equal to the mile marker m.
Both of these inequalities show the range of mile markers you can reach from El Reno based on the amount of fuel in your vehicle.