Mark M. answered • 09/08/19

Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

Let x = distance of car A from point C at time t

y = distance of car B from point C at time t

z = distance between the cars at time t

Given: dx/dt = -100 and dy/dt = -90

Find: dz/dt when x = 64 and y = 61

x^{2} + y^{2} = z^{2}

When x = 64 and y = 61, z = √[64^{2} + 61^{2}] = √7817

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

dz/dt = [x(dx/dt) + y(dy/dt)] / z = -11890/√7817 = -134.48

The cars are approaching each other at the rate of 134.48 mph when car A is 64 miles from the intersection and car B is 61 miles from the intersection.