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.
Henry has already answered the essential part of this question
http://www.jiskha.com/display.cgi?id=1297701375
To find the distance between mile marker 23 in Sayre, Oklahoma, and mile marker 125 in El Reno, Oklahoma, you need to subtract the smaller mile marker from the larger one.
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 move on to the next part of your question about the inequality for the mile markers you can reach from El Reno, given the amount of fuel (g) in your vehicle.
First, let's assume that your vehicle always gets 32 miles per gallon (mpg). This means that for every gallon of fuel you have, your vehicle can travel 32 miles.
To find the range of mile markers you can reach from El Reno, both in the forward and reverse directions, we need to consider two scenarios:
1. The maximum distance you can travel with the given amount of fuel:
In this scenario, you need to divide the amount of fuel (g) by the fuel efficiency (32 miles/gallon) to find the maximum distance you can travel.
Maximum distance = (amount of fuel) / (fuel efficiency)
Maximum distance = g / 32
Therefore, the mile marker you can reach from El Reno in the forward direction is Mile Marker (125 + maximum distance) and in the reverse direction is Mile Marker (125 - maximum distance).
2. The minimum distance you can travel with the given amount of fuel:
In this scenario, you need to divide the amount of fuel (g) by the fuel efficiency (32 miles/gallon) to find the minimum distance you can travel.
Minimum distance = (amount of fuel) / (fuel efficiency)
Minimum distance = g / 32
Therefore, the mile marker you can reach from El Reno in the forward direction is Mile Marker (125 + minimum distance) and in the reverse direction is Mile Marker (125 - minimum distance).
Putting it all together, the inequality that shows the mile markers (m) you can reach from El Reno, traveling in either direction, when g is the amount of fuel, in gallons, in your vehicle is:
125 - (g / 32) ≤ m ≤ 125 + (g / 32)