Related Rates - The Railroad Intersection (2 of 2): Better Approach

[lovelygirl]

I think the many variable approach isn't that bad. Actually, I find the algebra is less tedious.

x^2=T^2+C^2
Differentiate with respect to t,
2x dx/dt = 2T dT/dt + 2C dC/dt
dx/dt = (T dT/dt + C dC/dt) / x --- (*)

When t=1,
T=30+50(1)=80
C=40+40(1)=80
x=sqrt(80^2+80^2)=80sqrt(2)
dT/dt=50
dC/dt=40

Substitute into (*),
dx/dt = (80*50 + 80*40) / [80sqrt(2)] = 90 /sqrt(2) = 45 sqrt(2)