Cars Rate Distance

Question

Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west at 12 mi/h. At what rate is the distance between the cars increasing four hours later?

Answer 1

r^2 = x^2 + y^2 where r is distance]

differentiate r, x, and y vs time. dr/dt is what we want

2r dr/dt = 2x dx/dt + 2y dy/dt dx/dt = 12 and dy/dt = 16 mph (distance is not a vector, so ignore signs)

this is not linear, we need x, y and r to calculate the rate. t = 4, x= 48 y = 64 and r = 80 miles

plug in !