What Does Change in Gradient Mean for Road Design?

[tomtomtom1]

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.

Homework Equations

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

 

[DarthRoni]

I believe you have the right idea. However, for part A of the question I am not sure if they are asking you to determine if the gradient of AB and BC combined (AC) would 1/500 or if they are considering the individual lines. Either way, I believe you have to right answer.

 

[STEMucator]

The first part of the question asks you to add the slopes : http://www.wolframalpha.com/input/?i=(1/169)+(1/410)+>+1/500

For part b) you just subtract them.