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Math Help - Two cars are approaching an intersection.

  1. #1
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    Two cars are approaching an intersection.

    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.

    a) Express the distance d between the cars as a function of time t.
    [Hint: at t = 0, the cars are 2 miles south and 3 miles east of the intersection, respectively.

    b) Use a graphing utility to graph d = d (t). For what value of t is d smallest?

    Answers:
    a) d (t) = √2500t^2 360t + 13
    b) d is smallest when t = 0.072 hr.

    I just need help with the A part. The B part is easily. I have a hard time setting up my f(x) part. I am not sure the answers are right in the book on this one I keep on getting something diffrent as my d(t).
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  2. #2
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    Got it...

    I got it... was reworking it today and had my numbers backwards..

    here how you get part a)

    (2-30t) + (3-40t)

    (4 - 120t + 900t) + (9 - 240t + 1600t)

    d(x) = √2500t - 360t +13
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  3. #3
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    Now take the derivative and set equal to zero to find the min.
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