calc

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A____________B 9 miles is between A and B?
at 3pm Andy began travelling South at a rate of 4mi/hr from point A
at the same time Bill began travelling West at a rate of 5mi/hr from point B to A
both stop wlking when Bill reaches point A
What time will the distance between Bill and Andy be minimized?

  • calc -

    Let A be (0,0) and B = (9,0)
    The distance d between Bill and Andy after h hours can be found using

    d^2 = (4h)^2 + (9-5h)^2
    = 16h^2 + 81 - 90h + 25h^2
    = 41h^2 - 90h + 81
    d = √(41h^2 - 90h + 81)

    dd/dh = (82h - 90)/√(41h^2 - 90h + 81)

    dd/dh = 0 when h = 90/82 = 1.1 hr = 1:06

    3:00 + 1:06 = 4:06

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