74. Road Grade

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.
I'm stuck I don't get it can you help. Whay do I need to find? Should I divide 2000ft. and -.12 to find the horizontal change?

slope is defined as rise/run

you are given a rise of 2000 ft, we don't know the run
so set up the ration 2000/run = 12/100
12run = 2000(100)
run = 200000/12 = 16 667 ft

Now I understand! Thank You So Much!!!

To find the horizontal change in your position, you need to multiply the vertical change by the slope of the road.

In this case, the slope of the road is -12/100, which represents the change in vertical distance (per 100 units of horizontal distance).

To approximate the horizontal change, multiply the vertical change (2000 feet) by the slope (-12/100):

Horizontal change = 2000 ft * (-12/100)

Simplifying the expression gives:

Horizontal change = -240 ft

Therefore, you would have descended approximately 240 feet horizontally along the mountain road.

To find the horizontal change in your position, you need to multiply the vertical distance you have descended by the slope (grade) of the road.

In this case, the slope is given as -12/100 or -0.12 (since -12/100 = -0.12). So, multiplying the vertical distance of 2000 feet by -0.12 will give you the horizontal change.

Horizontal change = Vertical distance * Slope
= 2000 feet * -0.12
= -240 feet.

Therefore, based on the given information, you would have descended 2000 feet vertically, resulting in a horizontal change of -240 feet.