Car A is traveling west at 60 mi/h and car B is traveling north at 40 mi/h. Both are headed for the intersection of the two roads. At what r

Question

Car A is traveling west at 60 mi/h and car B is traveling north at 40 mi/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.4 mi and car B is 0.3 mi from the intersection?

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Thạch Thảo 3 years 2021-08-08T10:44:55+00:00 1 Answers 25 views 0

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  1. Tryphena
    0
    2021-08-08T10:46:41+00:00
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    Answer:

    Explanation:

    Let the car A be at distance x and car B be at distance – y  from origin (00) Distance between them be r so that , r = √( .4² + .3²) = .5 mi

    r² = x² + y²

    differentiating on both sides

    2r dr/dt = 2 x dx/dt + 2 ydy / dt

    r dr/dt =  x dx/dt +  ydy / dt

    r dr / dt = .4 x 60 + .3 x 40

    .5dr / dt = .4 x 60 + .3 x 40

    dr / dt = (24 +12 )/ .5

    = 72 mi / h

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