Problem: You have a choice of climbing one of three geometrically shaped mountains. One of the mountains is a perfect cylinder, another is in the shape of a cone, and the third looks like the top half of a sphere. Several out-of-work math teachers have constructed roads that go from the base to the summit of each mountain. All three roads are built so that you climb $1$ vertical foot with every $20$ horizontal feet. If you wish to walk the shortest distance from base to summit, which mountain would you choose?
My Questions: Since the ratio is the same for all the mountains ($1$ vertical ft : $20$ horizontal ft), wouldn't you have to walk $200,000$ horizontal ft no matter which mountain you choose? Is that even what this question is asking?