If you reach a city on interstate and vehicle can travel on 32 mpg. write an inequality that shows the mile makers (m)you can reach from city at mile marker 125 going in either direction,when g is the amount of fuel , in gallons, in your vehicle. explain what this means (east is higher mile markers and west is less mile markers)
To write an inequality that shows the mile markers you can reach from a city at mile marker 125, given that your vehicle can travel at a rate of 32 mpg and you have g gallons of fuel, we need to consider the distances you can travel in each direction.
When traveling east (higher mile markers), you can calculate the maximum distance you can travel by multiplying the rate of 32 mpg by the amount of fuel, g. This gives you an expression for the distance east you can travel:
Distance East = 32 * g
To find the mile marker you can reach when starting from mile marker 125 and traveling east, you need to add the distance traveled east to the initial mile marker. Thus, the inequality can be written as:
Mile Marker ≤ 125 + (32 * g) (Note: ≤ is used instead of < because you can also reach the mile marker you start from)
Similarly, when traveling west (lower mile markers), you can use the same expression for the distance traveled west:
Distance West = 32 * g
To find the mile marker you can reach when starting from mile marker 125 and traveling west, you need to subtract the distance traveled west from the initial mile marker. Thus, the inequality can be written as:
Mile Marker ≥ 125 - (32 * g)
In summary:
1. Traveling East: Mile Marker ≤ 125 + (32 * g)
2. Traveling West: Mile Marker ≥ 125 - (32 * g)
This means that, depending on the fuel in your vehicle, the inequality gives you the range of mile markers you can reach from the city at mile marker 125. The greater the amount of fuel (g), the farther you can travel in both directions (east and west) from the starting point.