Two cars, car X and car Y , start moving from the same point P on a cross intersection. Car X is travelling east and car Y is tr
avelling north. Some time later car X is 60 km east of point P and travelling in an easterly direction at 80 km/h and car Y is 80 km north of point P and travelling in a northerly direction at 100 km/h. How fast is the distance between car X and car Y changing?
Let the distance traveled by car X be x km <span>let the distance traveled by car Y by y km </span> <span>their paths form a right-angled triangle. </span> <span>Let the distance between them be D km </span> <span>D^2 = x^2 + y^2 </span> <span>2D dD/dt = 2x dx/dt + 2y dy/dt </span> <span>dD/dt = (x dx/dt + y dy/dt)/D </span>