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Math Help - Practical Optimization Word Problem

  1. #1
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    Post Practical Optimization Word Problem

    It is noon, and the spy is back from space and driving a jeep through the sandy desert in the tiny principality of Alta Loma. He is 32 kilometers from the nearest point on a straight paved road. Down the road 16 kilometers is a power plant in which a band of international terrorists has placed a time bomb set to explode at 12:50 pm. The jeep can travel 48km/hr in the sand and 80 km/hr on the paved road. If he arrives at the power plant in the shortest possible time, how long will our hero have to defuse the bomb?

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  2. #2
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    Now the way I've read that is that he is on the sand, and he needs to drive 32km on the sand to get to the straight paved road which is 16km to the power plant...but seeing as how dodgy the 2nd sentence is there, I'll do it in reverse as well.

    So the first way;
    1. 32km @ 48km/h
    2. 16km @ 80km/h

    1. t=32/48 hours
    t=2/3 hr = 40min (by doing 2/3 times 60)

    2. similarly t=16/80 = 12 min

    so the total time is 52mins, he starts at noon, he's 2 mins late.


    And the second way;
    1. 32km @ 80km/h
    2. 16km @ 48km/h

    1. t=32/80 hrs = 24min

    2. t=16/48 hrs = 20min

    total time is 44mins so he's got 8minutes left.


    ...Now it just depends if you're an optimist, a pessimist or if you can interpret that 2nd sentence better.

    My reasoning for picking the first way was that; it says he's 32km from said road, and that said road is 16km, so the 32km must be the sand??
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