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Can you help me with a question regarding topographic map reading?

Question number 4 in my lab book asked me to find the map distance between the highest point (1,335 feet) and the lowest point (660 feet). The answer I found was 675 feet (1,335-660=675). The next question asks, "if you walked along the line described in question 4, would the actual distance walked be greater, less, or the same as the map distance? Explain. I'm clueless.

Public Comments

1. greater, as you are also descending as well as going the map distance
2. The map distance you found is "as the crow flies". It's a straight line with no horizontal change. But if you actually walk from the top of a mountain to the bottom, you're not just walking in the horizontal direction; you're also walking vertically. So you would cover a greater distance because you're walking the same amount horizontally and a higher amount vertically. Think of a ramp that is 10 ft tall and 20 ft long at the base. If you walk on flat ground next to the ramp, you walk 20 ft. But if you walk on the ramp, you walk a greater distance because you are walking the hypotenuse of a triangle. I hope this makes sense!
3. The distance you have calculated is the vertical height of the summit, what you are being asked for (I think) is the horizontal distance on the map between the two points. You need to measure this accurately and use the map's scale to work out the distance on the ground. The second part of the question requires you to think in three dimensions. The flat map is representing a hilly or mountainous region that has altitude. The altitude at various points is shown on the flat map by the contours. Effectively the mountain is a cone, you have calculated the vertical height and measured the horizontal distance of the base, but if you walk this line you'll be walking up the inclined face of the cone. Is that greater, the same, or less than the horizontal distance?