Question

The maximum grade allowed between two stations in a​ rapid-transit rail system is​ 3.5%. Between station A and station​ B, which are 270 ft​ apart, the tracks rise 8 and one half 8 1 2 ft. What is the grade of the tracks between these two​ stations? Round the answer to the nearest tenth of a percent. Does this grade meet the​ rapid-transit rail​ standards?

Answer 1

Answer:

x = 3.1 %

Step-by-step explanation:

Let x be the slope the track.

Given:

Distance between station A and B = 270 ft

Track rise = $8\frac{1}{2} = \frac{17}{2} = 8.5\ ft$

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

Solution:

The maximum grade allowed between two stations in a​ rapid-transit rail system is​ 3.5%.

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

$Slope\ of\ the\ the\ tracks =\frac{Distance\ between\ two\ stations}{track\ rises}$

$x=\frac{8.5}{270}\times 100$

x = 3.1 %

So x = 3.1 % less than the maximum grade allowed between two stations in a​ rapid-transit rail system is​ 3.5%.

Therefore, x = 3.1 % meets the​ rapid-transit rail​ standards.