Suppose,
x = distance of the man
s = length of the shadow
Using the idea of similar triangles
6/s = 23/(x + s)
Simplifying:
we get,
6(x + s) = 23s
6x + 6s = 23s
6x = 17s
Differentiating with respect to time,
6(dx/dt) = 17(ds/dt)
Manipulating the above equation for ds/dt,
ds/dt = (17/6)(dx/dt)
ds/dt = (17/6)(6)
ds/dt = 17 ft/sec.
