Question

The maximum grade allowed between two stations in a rapid-transit rail system is 3.6%. Between station A and station B, which are 220 feet apart, the tracks rise 6 ft. What is the grade of the tracks between these stations? Round the answer to the nearest tenth of a percent. Does this grade meet the rapid-transit rails standards?

Answer 1

From the question, we are given that the distance between Station A and B = 220 feet

The track rise is 6 feet

We need to find the slope of the railway track between station A and B

The maximum grade allowed between two stations in a rapid-transit system is 3.6%

We know that the slope of the railway track is equal to the gradient of the tracks.

So, the slope of the railway track is defined as the ratio of the distance between the stations and track rises.

Which is

`\begin{gathered} Slope\text{ of the tracks = }\frac{Track\text{ rise }}{distance\text{ between two stations}} \\ =(6)/(220) \\ x=(6)/(220)*100 \\ x=2.72727 \\ x=2.73\% \end{gathered}`

So, x = 2.73%

Hence the grade of the tracks between these​ stations is 2.73%

This is less than the maximum grade 3.6% allowed between two stations in a rapid-transit rail system.

Hence this meets the rapid-transit rail standards