Question

A road has a gradient of 1/5 for 90 m. Then there is a horizontal section 130 m long. The final section has a gradient of 1/5 for 200 m.
a Find the total height gained from start to finish.
b What is the average gradient from start to finish?

Answer 1

Answer:

Total height gained from start to finish is 14 m

Step-by-step explanation:

Solution:

Let height1 as the height for 1/15 gradient.

By substituting in the following formula

Gradient = Rise/Run

1/15 = heights/90

so, height1 = 6m

Let height2 as the height for horizontal section.

As it is horizontal there is no height.

So, height2 = 0 m.

Let heigt3 as the height for  1/25 for 200m.

Gradient = Rise/Run

so, 1/25 = height3/200

height3 = 8 m.

So, Total height = height1 + height2 + height3

Total height = 6m + 0m + 8m

so, Total height = 14m

Answer 2

Given:

A road has a gradient of 1/5 for 90 m.

horizontal section 130 m long

The final section has a gradient of 1/5 for 200 m.

First we have to find the total height gained from start to finish

total height from start to finish=   $90\times\frac{1}{5} +200\times\frac{1}{5}$

$=18 + 40$

total height from start to finish =58 m

the average gradient from start to finish= $\frac{58}{90+130+200}$

$=\frac{58}{420} \\=\frac{29}{210}$

Hence the total height gained from start to finish is 58m and the average gradient from start to finish is 29/210