Two trains leave a station at the same time. One travels north on a track at 30 mph. The second travels east on a track at 60 miles per hour. How fast are they traveling away from one another in miles per hour when the northbound train is 60 miles from the station?

Question

mertsj · Answer

D^2=x^2+y^2 where x is northbound train and y is eastbound train
dx/dt=30
dy/dt=60
Differentiating:
2DdD/dt=2xdx/dt+2y/dydt or
D dD/dt=x dx/dt +y dy/dt
D^2=30^2+60^2=4500
D=67.08
67.08 dD/dt=60(30)+120(60)   since t = 2
dD/dt=134.17 mph

anonymous · Answer

Hmmm it says it's not right?

mertsj · Answer

Maybe you need to round it differently.  What do the directions say?

hero · Answer

@Mertsj you made a mistake

hero · Answer

D(2) = 134.17

D'(2) = 67.082