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Math Help - Optimization: Ms. Red

  1. #1
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    Optimization: Ms. Red

    Ms. Red is taking the trip to her foolish Grandma in the least amount of time. Grandma lives 6 miles east and 4 miles south of Ms. Red. And Ms. Red walks at a speed of 5 mph along the road and 3mph through the forest. What is the least amount of time it takes Ms. Red to get to her Grandma's house?
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  2. #2
    MHF Contributor

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    Re: Optimization: Ms. Red

    Are you sure that is all there is to the problem? If the road goes directly to Grandma's house, and Grandma lives \sqrt{36+ 16}= \sqrt{52} miles away, Ms Red could get there in \frac{\sqrt{52}}{5} hours. That is the "least amount of time" she could take. But I suspect there is more to the problem, than that! Is there some geometry here? Where does the forest lie in relation to the two houses and the road?
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