William W. answered • 12/08/19

Experienced Tutor and Retired Engineer

Draw a picture:

Using similar triangles, we can say:

Cross multiplying, we get:

12(l - x) = 5.5l

12l - 12x = 5.5l

6.5l = 12x

x = (6.5/12)l

Taking the derivative with respect to time we get:

dx/dt = (6.5/12)dl/dt or

dl/dt = (12/6.5)(dx/dt)

We know dx/dt = 2 so dl/dt = (12/6.5)(2) = 24/6.5 = 48/13 ft/sec

For question 2, just subtract the rate the shadow is going from the rate the man is going so 48/13 - 2 = 22/13 ft/sec.

Notice that the 25 foot distance doesn't matter in this problem.