Find the speed at which the distance is increasing between two cars, two hours after start.

Question

Two cars start at the same location and at the same time. Car A travels north at 8 mph, and car B travels east at 6 mph. Find the speed at which the distance between the two cars is increasing 2 hours after the start.

Answer 1

Here we're relating the speed that car A is traveling, the speed that car b is traveling and the speed in which the distance between the cars is increasing.

So we're relating dA/dt, dB/dt and dD/dt where A is the distance traveled by car A, B is the distance traveled by car B and D is the distance between the cars.

Thus, we have to find a way to relate A, B, and D

Notice that these three distances form a right triangle.

A is the vertical side, B is the horizontal side and D is the hypotenuse.

Thus we can relate A, B, and D with the pythagorean theorem

A² + B² = D²

Now take the derivative with respect to t

2A*dA/dt + 2B * dB/dt = 2D * dD/dt

Lastly plug in the values

Get the distance that A and B traveled two hours after the start

Find how far they are apart from each other two hours after the start