微積分章節，相關變率問題，請問圈起來的題目如何解?

(a)
設影子的長度為L
當人距離路燈的基座 10 ft 時
5 / 15 = 1 / 3 =L / ( L + 10 )
3L = L + 10
L = 5
d( 影子尖端 , 路燈基座 ) = 5 + 10 = 15

設 Δt 之後, 人往前走了 Δx , 影子尖端往前移動了 Δy
此時, 影子長度 = (15+Δy) - (10+Δx) = 5+Δy-Δx
5 / 15 = 1 / 3 = (5+Δy-Δx) / (15+Δy)
3(5+Δy-Δx) = 15+Δy
15 + 3Δy - 3Δx = 15 + Δy
2Δy = 3Δx
Δy/Δt = (3/2)(Δx/Δt) = (3/2)*5 = 7.5

(b)
L(0) = 5
L(Δt) = 5+Δy-Δx
ΔL/Δt = [ (5+Δy-Δx) - 5 ] / Δt = Δy/Δt - Δx/Δt = 7.5 - 5 = 2.5

Ans:
(a) 7.5 ft/sec
(b) 2.5 ft/sec