Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?

Answer 1

Let x be the west bound car distance and y be the south bound car distance from the starting point. Let s be the distance between the two cars.

dx/dt = 20

dy/dt = 40

Need to find ds/dt after 4 hours

s² = x²+y²

Do implicit derivation

2s ds/dt = 2xdx/dt +2ydy/dt

ds/dt = (xdx/dt + ydy/dt)/s

After 4 hours, x = 4(20) = 80 miles and y = 4(40) = 160 miles.

s = √(80²+160²) = √32000 ≈ 178.89

ds/dt = (80)(20)+(160)(40)/√32000

= 8000/√32000 ≈ 44.72 mph