To find the vertical change in your position while driving on a road with a 6% uphill grade over a distance of 200 feet, follow these steps:
1. Understand the Grade Percentage: The grade percentage of 6% indicates the ratio of vertical change to horizontal distance. Specifically, it means there is a 6-foot rise for every 100 feet of horizontal distance.
2. Convert the Grade Percentage to a Decimal: The grade percentage of 6% can be written as a decimal by dividing by 100:
[tex]\[
\frac{6}{100} = 0.06
\][/tex]
3. Set up the Proportion: You need to find the vertical change over a distance of 200 feet. Using the ratio given by the grade:
[tex]\[
\text{Vertical Change} = 0.06 \times 200
\][/tex]
4. Calculate the Vertical Change: Multiply the decimal grade by the horizontal distance:
[tex]\[
0.06 \times 200 = 12
\][/tex]
Therefore, when you drive 200 feet on a road with a 6% uphill grade, the amount of vertical change in your position will be approximately 12 feet.
