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 distance you would need to travel from mile marker 23 in Sayre, Oklahoma, to mile marker 125 in El Reno, Oklahoma, you would subtract the starting point from the ending point:
Distance = Mile marker 125 - Mile marker 23
Distance = 125 - 23
Distance = 102 miles
So, you would need to travel 102 miles to reach mile marker 125 in El Reno, Oklahoma.
Now, let's move on to the second part of your question about the inequality that shows the mile markers you can reach from El Reno when considering the amount of fuel in your vehicle.
Let's assume that g represents the amount of fuel, in gallons, in your vehicle. Since your vehicle can travel 32 miles per gallon, we need to assess the distance you can travel based on the fuel available.
If your vehicle can travel 32 miles per gallon, then you can travel g gallons times 32 miles per gallon:
Distance = g * 32
Now, let's consider the inequality:
m ≤ Distance
This inequality indicates that the mile marker, m, must be less than or equal to the distance you can travel. It means that any mile marker, m, that is within the range of the distance you can travel from El Reno is included in the solution.
For example, if you have 3 gallons of fuel, you can travel a maximum of 3 * 32 = 96 miles. So, any mile marker that is 96 miles or less away from El Reno would be included in the solution.
In summary, the inequality m ≤ Distance represents the mile markers you can reach from El Reno, traveling in either direction, based on the amount of fuel, g, in your vehicle.