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2 September, 00:38

4. Two ships leave port at the same time. One sails south at 15 mi/h, and the other sails east at 20 mi/h. Find a function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

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  1. 2 September, 00:46
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    (D = 25t) is the function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

    Explanation:

    First ship sailed south at a speed of 15 mi/h, let this be = A

    Second ship sailed east at a speed of 20 mi/h, let this be = B

    Making a sketch of the position of this two ships, we will obtain a right angled triangle.

    The distance between the two ships is the hypotenuse of the right angled triangle, let this be = D

    From Pythagoras theorem

    D² = A² + B²

    To find a function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

    ⇒ D² = (At) ² + (Bt) ²

    D² = (15t) ² + (20t) ²

    D² = 225t² + 400t²

    D² = 625t²

    D = √625t²

    D = 25t

    Therefore, (D = 25t) is the function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.
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