Pre cal help please!?

Question

When driving down a mountain road, you notice warning signs indicating that it is a "12% grade." This means that the slope of the road is -12/100. Approximate the amount of horizontal change in your position if you note from elevation markers that you have descended 2000 feet vertically.

thanks!!

Answer 1

A slope of -12/100 is a ratio that means that for every 100 feet horizontally (run or x-axis) you travel (note: NOT feet traveled down the slope), you'll descend 12 feet vertically (rise or y-axis).

Simplest way to solve this problem is to think that for every 12 feet you descend, you've traveled 100 feet, so by the time you descend 2000 feet, you will have traveled a proportionate distance x.

Just set up your ratio and cross-multiply to solve:

2000/x = 12/100

12x = 200,000

x = 16,666 feet