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, travelling in either direction, when g is the amount of fuel, in gallons, in your vehicle. Explain what this means.
El Reno is 125-40 = 85 mi from Sayre.
mileage is mi/gal
You want miles, knowing gallon
mi = mi/gal * gal = 32g mi
Yiu are now at m 125, so with g gal, you can reach m 125 ± 32g
To find out the distance between mile marker 23 in Sayre, Oklahoma, and mile marker 125 in El Reno, Oklahoma, you can subtract the two mile marker values:
Distance = Mile Marker 125 - Mile Marker 23
Distance = 125 - 23
Distance = 102 miles
Therefore, you would need to travel 102 miles to reach mile marker 125 in El Reno, Oklahoma.
Now, let's consider the fuel situation. If your vehicle can travel 32 miles per gallon, you can determine how many miles you can travel based on the amount of fuel (gallons) in your vehicle.
Let's represent the distance (m) you can travel from El Reno as an inequality, where g represents the amount of fuel in your vehicle (in gallons):
m ≤ g * 32
This inequality means that the distance (m) you can reach from El Reno, in either direction on the interstate, is less than or equal to the amount of fuel (g) in your vehicle multiplied by 32, which represents the number of miles your vehicle can travel per gallon.
In simple terms, the inequality shows that the distance you can travel from El Reno, Oklahoma, is restricted by the amount of fuel you have in your vehicle. The more fuel you have, the further you can travel.
To calculate the distance between mile marker 23 in Sayre, Oklahoma, and mile marker 125 in El Reno, Oklahoma, we can subtract the initial mile marker from the final mile marker:
Distance = Mile marker 125 - Mile marker 23 = 125 - 23 = 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 the question.
To write an inequality showing the mile markers you can reach from El Reno, let's first consider the scenario where you have a full tank of fuel, which can travel 32 miles per gallon.
Since you have enough fuel to travel 32 miles per gallon, the number of miles you can travel is directly proportional to the number of gallons of fuel in your vehicle.
Let's denote the amount of fuel in gallons as "g" and the number of miles you can travel as "m."
So, the inequality that represents the mile markers you can reach from El Reno, traveling in either direction, would be:
|m - 125| ≤ 32g
This inequality says that the absolute value of the difference between the mile marker you want to reach (m) and the mile marker you are currently at (125) can be no greater than 32 times the amount of fuel you have (g). This means that if the difference between the mile marker you want to reach and the mile marker you are currently at is less than or equal to 32 times the amount of fuel you have, you will have enough fuel to reach your desired mile marker.
For example, if you have 2 gallons of fuel (g = 2), the inequality becomes:
|m - 125| ≤ 32(2)
|m - 125| ≤ 64
This means that if the difference between the mile marker you want to reach and the mile marker you are currently at is less than or equal to 64 (which is 32 miles * 2 gallons), you will have enough fuel to reach your desired mile marker.