Question

A car A is travelling from west at 50 km/hr and car B is travelling towards north at 60 km/hr. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.3 kilometers and car B is 0.4 kilometers from the intersection?

Answer 1

We draw diagram where C is the intersection of the two roads. At a given time t, let x be the distance from car A to C, let y be the distance from car B to C and let z be the distance between the cars A and B where x, y and z are measured in kilometers. 

We are given that dx/dt = -50 km/hr and dy/dt = -60 km/hr

Note that x and y are decreasing and hence the negative sign. 

We are asked to find dz/dt

The equation that relate x, y and z is given by the pythagoras theorem z² = x² + y² 

Differentiating each side with respect to t,

We have

i.e., 

The cars approaching each other at a rate of 78 km/hr.