a sign on a highway says 6% grade, next 3 miles. this means that the slope of the road ahead is 6/100. how much will you climb in elevation ( in feet) over the next 3 miles
3(.06) = 0.18 miles
To determine how much you will climb in elevation over the next 3 miles with a slope of 6%, you will need to calculate the vertical rise. Here's how you can do it:
1. Start by converting 6% to the decimal form. Divide 6 by 100 to get 0.06.
2. Multiply the decimal form of the slope by the total horizontal distance, which is 3 miles. 0.06 x 3 = 0.18.
3. The result of this calculation, 0.18, represents the ratio of vertical rise to horizontal distance. This means that for every 0.18 units of horizontal travel, there will be a 1 unit increase in elevation.
4. Since you're traveling 3 miles, you need to convert miles to feet. As there are 5,280 feet in a mile, multiply 3 by 5,280 to get 15,840 feet.
5. Multiply the total distance in feet (15,840) by the ratio of vertical rise (0.18). 15,840 x 0.18 = 2,851.2.
6. The result, 2,851.2 feet, is the amount of elevation you will climb over the next 3 miles.
Therefore, you will climb approximately 2,851.2 feet in elevation over the next 3 miles with a 6% grade.