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Help With A Gradient Problem

  1. Oct 14, 2013 #1
    Hi all

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


    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    NA

    3. 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
     

    Attached Files:

  2. jcsd
  3. Oct 14, 2013 #2
    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.
     
  4. Oct 14, 2013 #3

    Zondrina

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