differentiate

(X^2 + 200^2)^(1/2) multiplied by (1/4), and substitute X=200tanY

and

((500-X)^2 + 200^2)^(1/2) multiplied by (1/3), and substitute

X= -200tanZ+500

then combine equations and show that the minimum time occurs when (sinY)/m = (sinZ)/n where m and n are constants