Actually Applicable Application Problems and Brainteasers/Wheelchair Ramp Standards

Overview
Wheelchair ramps cannot be too steep or they will be too difficult for wheelchair users to roll up, and the wheelchair may collect an unsafe amount of momentum in rolling down. The standard is that the slope may be up to $$ \frac{1}{12}$$, meaning that for each 1 foot up, the ramp must go at least 12 feet forward. (The same ratio will work with any unit of measurement, so you can use inches instead of feet, or meters, centimeters, etc.) Flatter is OK; steeper is not.

This type of calculation is Actually Applicable for building planners and construction workers, who use this strategy to find out whether existing ramps need to be replaced and check whether a planned ramp meets the standards, as well as for anyone who cares about making sure their community locations are safe for wheelchair users.

General Method

 * 1) Measure the vertical change between the top and bottom of the ramp.
 * 2) Measure the horizontal change between the top and bottom of the ramp.
 * 3) * You may need to get clever to take these measurements, such as by using a plumbline, bubble level, something with a fixed 90 degree angle, etc.
 * 4) Divide the vertical change by the horizontal change to find the ramp's slope.
 * 5) Compare the slope with the standard to make sure it is not over the limit.

Problems

 * Does a ramp with a vertical change of 8" and a horizontal distance of 6' meet the standard?
 * Does a ramp with a vertical change of 2' and a horizontal distance of 30' meet the standard?

Make Your Own Problem
Measure a ramp in your community and perform the calculations to make sure it is accessible.

Is the ramp in the picture at https://themighty.com/wp-content/uploads/2017/09/img_2394-1280x640.jpg likely to be accessible? Use measurements from a typical staircase to decide.

Related Problems
Wheelchair Ramp Standards 2 is about using trigonometry to get around a common measurement complication.