Question

Car A is going 30 km/h on Loon Street and car B is going 40 km/h on Duck Avenue. Both cars are
heading towards the intersection of the street and avenue (at 90 degrees) . At which rate is the distance between the cars decreasing when car A is 0.15 km and car B is 0.2 km from the intersection? (Picture below)

Answer 1

Write a parameterization of the x and y cars as such:
x = -0.15 + 30t
y = -0.20 + 40t

Answer 2

Now, you can work with the distance formula (or Pythagoras' Theorem if it pleases you) to notice that the distance, D, between the two cars is given by: \[D^{2}=x^{2} + y^{2}\]

Answer 3

Use the chain rule to take the derivative of both sides of the equation.
\[2D*dD/dt =2x* dx/dt +2y* dy/dt\]
Solve for dD/dt

Answer 4

This is really helpful, but I'm still a little confused about "parameterization." Could you elaborate a little bit on how those two equations were derived?

Answer 5

Let me see if I understand the parameterization part:

If I pretend that cars A & B are moving away from the corner as opposed to towards it, their distances would respectively be (30t - 0.15) & (40t -0.2).

Is that where that comes from?