A lamp hangs at a height of 4m directly on a street if on that street a 1.5 m tall person? walks away

walks away from the lamp at the rate of 55 m/min how many m/min is lengthened the shadow ??
the answer is 33 m/min

Did you copy this question out of a textbook?
The grammar is not great, so I hope I understood what you're asking.

Draw a diagram with similar triangles: ABE and CDE, where
A = top of lamp post
B = bottom of lamp post (at ground level)
C = top of person
D = bottom of person
E = tip of shadow

AB = 4 m
CD = 1.5 m
BD = x = distance from person to lamppost ---> dx/dt = 55 m/min
DE = y = length of shadow ---> dy/dt = rate we are trying to calculate

By similar triangles:
AB/BE = CD/DE
4/(x+y) = 1.5/y
4y = 1.5x + 1.5y
2.5y = 1.5x
y = (1.5/2.5)x
y = 0.6x

Differentiate both sides with respect to t
dy/dt = 0.6 dx/dt
dy/dt = 0.6 * 55 m/min
dy/dt = 33 m/min

Length of shadow is increasing at a rate of 33m/min

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