Question

The halfway point of a tunnel through a mountain is 3/2 miles from either end of the tunnel. The mountain is 660 feet (1/8 miles) high. Find the slope of the side of the mountain

Answer 1

Hi, and welcome to QuestionCove!

It seems like this question is modeling the mountain as a triangle, like the diagram I've drawn (please excuse the horrendous scale)
To find the slope of the mountainside, we only need to take the height of the mountain divided by the horizontal distance it takes to reach that height.
In other words,

Slope = height/horizontal distance.

In this case, the height is 1/8 mile, and the horizontal distance is 3/2 mile.
So, the slope will be equal to (1/8) / (3/2)
= 1/12 mile