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Math Help - Cars

  1. #1
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    Cars

    Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the intersection and is moving at a constant speed of 40 miles per hour. Express the distance d between the cars as a function of time t.

    HINT GIVEN:

    At t = 0, the cars are 2 miles south and 3 miles east of the intersection, respectively.
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  2. #2
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    Hello, blueridge!

    Did you make a sketch?


    Two cars are approaching an intersection.
    One is 2 miles south of the intersection X and is moving north at 30 mph.
    The other car is 3 miles east of X and is moving west at 40 mph.
    Express the distance d between the cars as a function of time t.
    Code:
            X  3-40t   B    40t    Q
            * - - - - - * - - - - - *
            |         /
            |       /
      2-30t |     / d
            |   /
            | /
          A *
            |
        30t |
            |
          P *

    The first car starts at P, 2 miles south of X\!:\;\;PX=2
    In t hours, it has moved 30t miles north to point A.
    . . Hence: . AX \:=\:2-30t

    The second car starts at Q, 3 mile east of X\!:\;QX = 3
    In t hours, it has moved 40t miles west to point B.
    . . Hence: . BX \:=\:3-40t

    From right triangle AXB, we have: . d^2 \:=\:AX^2 + BX^2

    So we have: . d \;=\;\sqrt{(2-30t)^2 + (3-40t)^2}

    . . which simplifies to: . d \;=\;\sqrt{2500t^2 - 360t +13}

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