Related Rate (Calculus)

Question

A police car is located 60 feet to the side of a straight road.

A red car is driving along the road in the direction of the police car and is 160 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 95 feet per second. How fast is the red car actually traveling along the road?

Answer 1

Draw a diagram. If the distance along the road is x, then the distance z from the car to the police car can be found via

z² = x^2 + 3600

So, when x=160, z = 20√73

That means we have

z dz/dt = x dx/dt

Plugging our number, we have

20√73 * -95 = 160 dx/dt

so the car's speed (dx/dt) is -95/8 √73

The negative sign indicates that the distance is decreasing as the car approaches.