K9-47G Posted November 13, 2005 Posted November 13, 2005 This is one optimization problem that I just cant figure out. I'll post what I have... A hiker at point A on a straight road wants to reach, in the shortest time, a point B located 6 miles from the road and 10 miles from point A. The hiker's speed on the paved road is 4 mph and only 2 mph off the road. How far should he continue on the road before heading in a straight line for the point B? I am pretty sure I would have to use the pythagorean theorem because if you draw the problem you get a triange with two sides given. Plus I denoted [math] dr/dt [/math] to be the speed on the road which is 4 mph, and [math] do/dt [/math] to be the speed off road which is 2 mph. I just don't know how to find my objective function. Any help would be appreciated.
TD Posted November 13, 2005 Posted November 13, 2005 You're on the right track. With your drawing, split the problem in 2 parts using an intermediate point P. Express the distance as a function of the distance to P by using the pyth. theorem on the triangle, compute the time necessary to do both parts with the given speeds and then add those two parts.
ecoli Posted November 13, 2005 Posted November 13, 2005 right... at want point p would the hiker be able to travel the distance the fastest?
TD Posted November 21, 2005 Posted November 21, 2005 I can't check your answer since the question isn't 100% clear to me. Is B located 6 miles under the road, vertically? So the distance between B and the road is 6. And the 10 miles, is that the (straight) distance between A and B or between A and the point on the road which is above B?
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