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Math Help - Interesting Problem: Geometry

  1. #1
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    Interesting Problem: Geometry

    There is a cuboid room with dimensions 6m, 5m, 8m.

    Find the shortest time taken by an ant inside the room, to go from A to B if the ant moves at a speed of 50cm/min
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  2. #2
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    Can the ant walk directly there? Or does it have to walk on the walls?

    The shortest distance that it has to travel if it has to walk on the walls is diagonally from the 2 longest sides and directly from the shortest side.

    So the distance that it has to walk is \sqrt{6^2 + 8^2} + 5 = ...
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  3. #3
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    Quote Originally Posted by rickrishav View Post
    There is a cuboid room with dimensions 6m, 5m, 8m.

    Find the shortest time taken by an ant inside the room, to go from A to B if the ant moves at a speed of 50cm/min
    If the back wall falls down that makes a length on the floor of (8+5) and 6 on a right angled triangle. The shortest distance must be the hypotenuse.

    so \sqrt{13^2 + 6^2}

    which is \sqrt{205} = 14.3m

    So at 50cm/m this would take 26.6 minutes
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  4. #4
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    Hello, rickrishav!

    There is a cuboid room with dimensions 6m, 5m, 8m.
    Find the shortest time taken by an ant inside the room, to go from A to B
    if the ant moves at a speed of 50 cm/min.

    The ant will move right and upward on the front face,
    then continue on the right face to \,B.


    Code:
          * - - - - * - - - * B
          |         |    *  |
          |         | *     |
          |        *|       | 8
          |     *   |       |
          |  *      |       |
        A * - - - - * - - - *
               6        5

    The distance is: . AB \:=\:\sqrt{11^2 + 8^2} \:=\:\sqrt{185} \:\approx\:13.6\text{ m}

    At 50 m/min, it will take 27.2 minutes.



    Brennan's answer has a typo; it should read 28.6 minutes.
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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, rickrishav!


    The ant will move right and upward on the front face,
    then continue on the right face to \,B.


    Code:
          * - - - - * - - - * B
          |         |    *  |
          |         | *     |
          |        *|       | 8
          |     *   |       |
          |  *      |       |
        A * - - - - * - - - *
               6        5

    The distance is: . AB \:=\:\sqrt{11^2 + 8^2} \:=\:\sqrt{185} \:\approx\:13.6\text{ m}

    At 50 m/min, it will take 27.2 minutes.



    Brennan's answer has a typo; it should read 28.6 minutes.

    Arr - I did not consider going your way - I went:
    Code:
          * - - - - * - - - * A
          |         |    *  |
          |         | *     |
          |        *|       | 6
          |     *   |       |
          |  *      |       |
       B * - - - - * - - - *
               8        5
    [size=3]
    lesson there is be thorough.
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