A streetlight is on a pole

Question

Give your answer accurate to 3 decimal places.

A streetlight is on a pole 15 ft tall. A boy 4 ft tall walks away from the pole at a rate of 4 ft/sec. At what rate is his shadow lengthening when he is 20 ft from the pole?

At what rate (in feet per second) is the tip of his shadow moving?

Answer 1

at time zero there was no shadow

in 1 second he's 4 feet from the pole

the shadow's tip moves from 0 to 4+16/11 = 5 5/11 feet from the pole

the tip moves at 5 5/11 feet per second regardless how far he is from the pole

construct two right triangles

set ratios of sides of the two similar right triangles equal

where x is how far the shadow's tip is from the boy

x/4 = (4+x)/15

15x=16+4x

11x=16

x=16/11

in 10 seconds the boy moved 10(4)= 40 feet

the tip moved 54 6/11 feet

a rate of 5 5/11 feet per second