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 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:

Part a) The grade is 3.2%

Part b) This grade meet the rapid-transit rail​ standard

Step-by-step explanation:

we know that

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this problem we have

$rise=8\frac{1}{2}\ ft=\frac{8*2+1}{2}=\frac{17}{2}\ ft$

$run=270\ ft$

so

$\frac{rise}{run}=\frac{17}{2}:270=0.0315$

convert to percentage

$0.0315*100=3.15\%$

Round to the nearest tenth of a percent

$3.2\%$

$3.2\% < 3.5\%$

therefore

This grade meet the rapid-transit rail​ standard