Question

Car A leaves an intersection at the same time as Car B. Car A is heading west at 50km/h and Car B is heading north at 70km/h. Determine the rate of change of the distance between the two cars after 20min
The "geometry" of this problem is a simple right-angled triangle.
At a time of t hours,
let the distance travelled north be 70t km
let the distance travelled west be 50t km
let the distance between them be d km

clearly,
d^2 = (70t)^2 + (50t)^2 = 7400t^2
d = √7400 t
dd/dt = √7400 <----- a constant
= 86.02 km/h

As long as they maintain the same speed in their same direction
they will separate at a constant rate of 86.02 km/h

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