you are driving up a long, inclined road . after 1.20 mi you notice that signs along the roadside indicate that your elevation has increased by 550 ft.
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3.7
To calculate the grade or slope of the road, you will need to use the elevation change and the horizontal distance traveled. In this case, the elevation increased by 550 ft over a distance of 1.20 mi.
Step 1: Convert the distance from miles to feet:
1.20 mi * 5280 ft/mi = 6336 ft
Step 2: Calculate the slope or grade:
Grade = (Elevation Change / Distance) * 100
Slope = (550 ft / 6336 ft) * 100
Step 3: Simplify the equation:
Slope = 0.0867 * 100
Step 4: Calculate the final result:
Slope = 8.67%
So, the slope of the road you are driving up is 8.67%.
To find the slope of the road, we need to determine the change in elevation per unit of horizontal distance. In this case, it is given that after traveling 1.20 miles, the elevation has increased by 550 feet.
To calculate the slope, we use the formula:
Slope = change in elevation / horizontal distance
Given that the change in elevation is 550 feet and the horizontal distance is 1.20 miles, we need to convert the units so that they are consistent. Since 1 mile equals 5280 feet, we can convert the distance as follows:
1.20 miles * 5280 feet/mile = 6336 feet
Now that the distance is in feet, we can calculate the slope:
Slope = 550 feet / 6336 feet ≈ 0.0869
Therefore, the slope of the road is approximately 0.0869.