Question

Help!!!

Please read the question first.

I want the process!!!
I want the process!!!
I want the process!!!

The correct answer is:
a. 1/6cm
b. 0.1cm

But why???

Antonio enjoys mountain biking. He has found that the maximum gradient which he can cycle up is 0.3 and the maximum gradient he can safely descend is 0.5. Antonio’s map has a scale of 2 cm to 1 km with contours every 25 m. What is the minimum distance between the contours (lines on a map showing the height of land) on his map that allows him to go.

a. What is the minimum distance between the contours on his map that allows him to go uphill?

b. What is the minimum distance between the contours on his map that allows him to go downhill?

Answer 1

Answer:

Step-by-step explanation:

contour lines on a map indicate elevation above sea level.

distance between contour lines on a map indicate how steep the terrain is.

gradient is an indication of steepness.

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contours every 25 meters means the elevation indicated by each contour line is 25 meters more or less then the adjoining contour line.

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gradient of 1 means 1 unit of vertical travel for 1 unit of horizontal travel.

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gradient of .5 means 1 unit of vertical travel for 2 units of horizontal travel.

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formula for gradient is g = y/x where g is the gradient, y is the amount of vertical travel, x is the amount of horizontal travel.

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maximum is calculated first.

.3 = 25 / x

this makes x = 25/.3 = 83.34 meters which represents the minimum distance between contour lines if the maximum gradient is .3

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minimum is calculated next.

.5 = 25 / x

this makes x = 25/.5 = 50 meters which represents the minimum distance between contour lines if the maximum gradient is .5

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I believe they are talking about real distances here, so we have to translate these real distances to distances on the map.,

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let's do going up first.

max gradient is .3

minimum distance between contour lines is 25/.3 = 83.34 meters.

83.34 meters is the same as .08334 kilometers.

scale of map is 2 centimeters per kilometer.

2 centimeters per kilometer * .08334 kilometers = .1667 centimeters which means the minimum distance between contour lines if he is going up.

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let's do going down next.

max gradient is .5

minimum distance between contour lines is 25/.5 = 50 meters.

50 meters is the same as .05 kilometers.

scale of map is 2 centimeters per kilometer.

2 centimeters per kilometer * .05 kilometers = .1 centimeters which means the minimum distance between contour lines if he is going down.