Trekking Uphill Is Much Easier On Paper Than In Real Life

Calculus Level 1

Sarah and Shane plan to hike from Mead Mountain, to checkpoint A, to Cove Hill, to checkpoint B and finally to Great Pond Mountain. They have plotted their course in green in the above topographical map, which shows contour lines at intervals of 20 meters.

Which of the following routes would they experience the steepest ascent ?

Image credit: Wikipedia
Mead Mountain to Checkpoint A. Checkpoint A to Cove HIll. Checkpoint B to Great Pond Mountain Cove Hill to Checkpoint B.

Chung Gene Keun by Chung Gene Keun , 42, USA

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10 solutions

Discussions for this problem are now closed

Arijit Banerjee
Mar 1, 2014

Geography in Brilliant! ... Brilliant work!...The more the lines closely spaced the steeper it is ... this is the basic concept of contour lines!

15 Helpful 0 Interesting 0 Brilliant 0 Confused

Well ICSE rocks, I know to read a topo map.

Bala Tweakbytes - 7 years, 3 months ago

Arijit, can you explain why it is steeper when the lines are closely spaced?

Arron Kau Staff - 7 years, 3 months ago

Contour lines represent a change in altitude. So in this case as mentioned above each next contour line represents a rise/drop in 20m altitude. So if 10 contour lines are 5cm apart on the map, compared to if 10 countour lines are 10cm apart on the map, the change in altitude is same for both but in 5cm it is at a shorter horizontal distance and so the slope is steeper

Aziz Sonawalla - 7 years, 3 months ago

Well I think its better if you see it in wikipedia ... While learning topo-map in my school I learnt about contour lines ...

Arijit Banerjee - 7 years, 3 months ago

Its just a convention that is followed while interpreting any map... this much I know!

Arijit Banerjee - 7 years, 3 months ago

contours are not a topic in Geography, it comes under Surveying.

Wahed Haiderally - 7 years, 3 months ago

well in icse we had it in Geography..

Arijit Banerjee - 7 years, 3 months ago

i did topography in cise .

Shashank Dobhal - 7 years, 3 months ago

Because this is the stepest way to pass checkpoint

Glenn Mark Gallego - 7 years, 3 months ago

Also be careful to notice that we're looking for a steep ascent, not descent. So we should check that the direction from B to the Mountain top is actually "uphill." It is!

Todd Richert - 7 years, 2 months ago

yes I consider like that also

Mohamed Sugule - 7 years, 3 months ago
Ashish Rao
Mar 7, 2014

As we look the map we observe that from point B to the hill, the lines are drawn very narrow. So obviously that path is going to be the steepest.No need for going for calculations, first think logically

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thats what I mean on the solution I posted

Carl De Guzman - 7 years, 2 months ago
Carl De Guzman
Mar 31, 2014

Count the lines that go through the path see what choice have the greatest number and its the answer Lines of the answer is:27

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Patrick Feltes
Mar 30, 2014

Contour lines have a certain distance that you can find on the map. For example, every line may be a five foot difference in height. So, if there are lines that are closer together, they will be steeper.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Saad Ahmad
Mar 26, 2014

As figure shows one line is 20 meters so the lines are very close from B mount . so it means if distance is not covered horizontally it must be vertically and it would be steepest here.

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Qamar Raj
Mar 13, 2014

simple bcz this is the long steepest ascent means lond height so this is right answer from B to midpoint

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Ankit Singh
Mar 9, 2014

Its easy, the steepness increases with the closeness of contour lines.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

actually before solving this problem, i didn't even know about topographical map..!! I think this problem provides enough information to solve....

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Achlesh Shivhare
Mar 7, 2014

contour lines r at interval of 20 i.e the difference between the altitude of two consecutive contour lines is 20.and there r too many closely spaced contour lines b/w b to pond mountain which indicates the number of lines multiplied by 20 gives the rise in altitude and the closely spaced lines shows the steepness or the lesser distance horizontally thus indicates the steepest portion .

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Eslam Hosny
Mar 6, 2014

its so easy

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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