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