Two cars start moving from the same point.

Question

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 is the distance between the cars increasing three hours later?

Answer 1

Start with a diagram showing the west travel and the south travel which makes a right triangle.

If W = West Travel which has a rate of 20mph and a value of 60 miles after 3 hours.

if S = South Travel which has a rate of 48mph and a value of 144 miles after 3 hours.

Let D = the distance between the 2 vehicles.

The travel triangle is W² + S² = D² Then (2D)dD/dt = (2W)dW/dt + (2S)dS/dt

or (D)dD/dt = (W)dW/dt + (S)dS/dt

D² = 60² + 144² , therefore D = 156, W = 60, dW/dt = 20, S = 144, dS/dt = 48

Substituting we get dD/dt = (60*20 + 144*48)/156 = 52 mph