# Help With A Gradient Problem

Hi all

I was hoping someone could help solve a gradient problem, I am more concerned about understanding what the question is asking me.

## Homework Statement

I have two straight lines which represents the vertical profile of a road.

Line AB has a gradient of 1 in 169 (for every 1 unit in the Y axis, you move 169 units in the X axis)

Line BC has a gradient of 1 in 410 (for every 1 unit in the Y axis, you move 410 units in the X axis)

The question is, if the Change In Gradient between the two lines exceeds 1 in 500 then the road must be re-designed.

A. Do the gradients of lines AB & BC exceed 1 in 500 – YES / NO.
B. What is the change in gradient between Lines AB & BC.

There are two parts of the question I am struggling to understand.
• The first bit is understanding the change in statement.
• The second bit is if the change in gradient is 1 in 600 for example then I would say that this is a shallower gradient and has not exceeded the 1 in 500 gradient threshold. If the change in gradient was 1 in 150 for example then this is a steeper gradient and has exceeded the 1 in 500 gradient threshold.

NA

## The Attempt at a Solution

From the statement “Change in” I would subtract the gradients of the two lines. So my first step would be:-

1/169 – 1/410 = 410/69290 – 169/69290 (I found a common denominator)

410/69290 – 169/69290 = 241/69290 (subtracted 410 – 169)

241/69290 = 1/ 287.5104 (rounded to 1 in 289)

Answer To Part A = YES the gradients has exceeded 1 in 500
Answer To Part B = The change in gradient is 1 in 289.

Is my thinking correct or have I got it wrong.

Any help will be greatly appreciated.

I have attached a sketch of the problem.

Thanks