there are 2 congruent right triangles whose sides have the same ratio
5/1.5 = the length from the base of the lamp post to the outer edge of the shadow divided by the shadow length. The length from the base to the shadow tip = the length of the shadow plus the distance the man is from the base of the shadow.
5/1.5 = (x+y)/x where x= shadow length and y= distance of the man from the lamppost
solve for x = 3y/7
take the derivative = rate of change of the shadow length
x'(t) = (3/7)y'(t) = (3/7)(2.7) = 8.1/7= 1.157 meters per second