The percent grade of a highway is the amount that the highway raises or falls in a given horizontal distance. For example, a highway with a four percent grade rises 0.04 mile for every 1 mile of horizontal distance.

a. How many feet does a highway with a six percent grade rise in 2.5 miles of horizontal distance?
b. How many feet would a highway with a six percent grade rise in 90 miles of horizontal distance if the grade remained constant?
c. How is percent grade related to slope?

a. Y/X = Y/2.5 = 0.06

Y/2.5 = 0.06
Y = 0.15 Miles = 792 Ft.

b. Y/X = Y/90 = 0.06
Y = 90 * 0.06 = 5.4 Miles = 28,512 Ft.

c. % Grade = Slope expressed as a decimal.

Correction:

c. % Grade = Slope expressed as a percentage.

a. To find how many feet a highway with a six percent grade rises in 2.5 miles of horizontal distance, we can use the given information that a four percent grade rises 0.04 mile for every 1 mile of horizontal distance.

First, let's find the rise in miles for a six percent grade. Since a four percent grade rises 0.04 mile, a six percent grade would rise 0.06 mile for every 1 mile of horizontal distance.

The rise in miles for 2.5 miles of horizontal distance would be calculated as follows:
Rise = 0.06 mile x 2.5 miles = 0.15 mile

Now, we need to convert the rise in miles to feet. Since 1 mile is equivalent to 5,280 feet, we can calculate the rise in feet as follows:
Rise in feet = 0.15 mile x 5,280 feet/mile = 792 feet

Therefore, a highway with a six percent grade would rise 792 feet in 2.5 miles of horizontal distance.

b. To determine how many feet a highway with a six percent grade would rise in 90 miles of horizontal distance, we can again use the given information that a four percent grade rises 0.04 mile for every 1 mile of horizontal distance.

First, let's find the rise in miles for a six percent grade. As mentioned before, a six percent grade rises 0.06 mile for every 1 mile of horizontal distance.

The rise in miles for 90 miles of horizontal distance would be calculated as follows:
Rise = 0.06 mile x 90 miles = 5.4 miles

Next, we convert the rise in miles to feet:
Rise in feet = 5.4 miles x 5,280 feet/mile = 28,512 feet

Therefore, a highway with a six percent grade would rise 28,512 feet in 90 miles of horizontal distance.

c. Percent grade is related to slope by representing the ratio of vertical distance to horizontal distance. It is typically expressed as a percentage or a decimal.

To convert percent grade to slope (as a decimal), the percent value is divided by 100. For example, a six percent grade is equal to a slope of 0.06 (6 divided by 100).

To convert slope back to a percent grade, the slope value is multiplied by 100. For instance, a slope of 0.06 is equivalent to a six percent grade (0.06 multiplied by 100).