A man 6 feet tall walks along a walkway which is 30 feet from a the base of a lamp which is 126 feet tall. The man walks at a constant rate of 3 feet per second. How fast is the length of his shadow changing when he is 40 feet along the walkway past
the closest point to the lamp?

My answer always is 3/20 but the right answer is 3/25. What can I do? Help me please!!!!!

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  1. When the man has walked a distance x, his distance d from the pole is

    d^2 = x^2+30^2

    If his shadow then has length s,

    s/6 = (d+s)/126
    d = 20s

    So, plugging that in,

    400s^2 = x^2+30^2
    at x=40, s = 5/2
    800s ds/dt = 2x dx/dt
    2000 ds/dt = 80*3
    ds/dt = 3/25

    When you get stuck, or cannot agree with the answer, it'd be nice for you to show your work, huh?

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