Calculus Word Problem

Question

Two cars are approaching an intersection on roads that are perpendicular to each other. Car A is north of the intersection and traveling south at 60 mph. Car B is east of the intersection and traveling west at 45 mph. How fast is the distance between the cars changing when car A is 14 miles from the intersection and car B is 48miles from the intersection? (Round your answer to two decimal places.) 

Answer 1

Let x = the position of car B at time t

and y = the position of car A at time t

x = 48-45t

y = 14-60t

d=sqrt(x² + y²)

dd/dt= [1/sqrt(x² + y²)][2x(dx/dt) + 2y(dy/dt)]

Now just plug the values in and get your answer

Make a picture.

B is driving west along the x-axis from (48,0) toward the origin at 45 mph.

A is driving south along the y-axis from (0,14) toward the origin at 60 mph.

The co-ordinates of each vehicle at time t are given by the 1st 2 equations.

d is the distance between them at any time t and dd/dt is the rate of change of that distance.

In the equation for dd/dt, x is 48, y is 14, dx/dt is -45 and dy/dt is -60.