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Math Help - Optimization

  1. #1
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    Optimization

    A snail, who can travel at 3 km/h hour is 10 km from the nearest point P on a straight highway. He wishes to travel to a point Q, 50 km along the highway from P, and she can arrange to have a turtle pick her up anywhere along the highway. The turtle travels at 15 km/h. What point on the highway should the snail head for as to arrive at Q in the shortest possible time?

    Wouldn't the snail want to be picked up at point P to get there the quickest?
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  2. #2
    Junior Member allsmiles's Avatar
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    LOL. loved your problem, it was so cute.

    anyway yes you are right. it should be picked up at point P.
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  3. #3
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    Quote Originally Posted by steezin View Post
    A snail, who can travel at 3 km/h hour is 10 km from the nearest point P on a straight highway. He wishes to travel to a point Q, 50 km along the highway from P, and she can arrange to have a turtle pick her up anywhere along the highway. The turtle travels at 15 km/h. What point on the highway should the snail head for as to arrive at Q in the shortest possible time?

    Wouldn't the snail want to be picked up at point P to get there the quickest?
    not at point P.

    make a sketch.

    let x = distance from point P where the snail hitches the ride.

    distance snail travels overland ... \sqrt{x^2+10^2}<br />

    distance snail travels on the highway with turtle ... 50-x

    t = \frac{\sqrt{x^2+10^2}}{3} + \frac{50-x}{15}<br />

    minimize t
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