cop car question

Question

A police car is located 30 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 210 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 75 ft/sec. How fast is the red car actually traveling along the road?

The actual speed (along the road) of the red car is how many  ft/sec

Answer 1

construct a right triangle with legs 50 and 210

hypotenuse = square root of 50^2 + 210^2

h^2 = b^2 + a^2 where a=210, b= 50, h = sqr(2500+44100)= sqr46600= 10sqr466=about 215.87

take the derivative

2hh' = 2bb' +2aa' b'=0, h' =75,

divide by 2, plug in the values

215.87(75) = 0 + 210a'

a' = 215.87(75)/210 = about 77.1 feet per second