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Math Help - Distance and Time Problem

  1. #1
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    Distance and Time Problem

    A train leaves a station at noon and travels east at the rate 30 mi/hr. At 2 P.M. of the same day a second train leaves the station and travels south at the rate 25 mi/hr. Express the distance d (mi) between the trains as a function of t (hr), the time the second train has been traveling.

    Given answer:
    d = 5\sqrt{61t^2-144t+144}

    I began with:
    d^2 = (30t)^2+(25(t-2))^2
    Am I incorrect?
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  2. #2
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    Nevermind... I found a way to the answer!

    I believe the correct way to start is:
    d^2 = (30(t+2))^2+(25t)^2
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by jesse View Post
    A train leaves a station at noon and travels east at the rate 30 mi/hr. At 2 P.M. of the same day a second train leaves the station and travels south at the rate 25 mi/hr. Express the distance d (mi) between the trains as a function of t (hr), the time the second train has been traveling.

    Given answer:
    d = 5\sqrt{61t^2-144t+144}

    I began with:
    d^2 = (30t)^2+(25(t-2))^2
    Am I incorrect?
    Note quite your model isn't valid for

     0 \le t \le 2

    When t=1 the trains should be 30 miles apart!
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  4. #4
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    It's from a book from the 50s. They were still trying to figure this whole math thing out back then.
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  5. #5
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    Hi jesse,
    At time zero eastbound is 60 miles out .southbound is 0 miles out
    after t hrs EB is 60 +30t miles out
    SB is 25t miles out
    d^2 =(60+30t)^2 + (25t)^2
    solve for d in terms of t


    bjh
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