Answer:
20 mi/h
Step-by-step explanation:
You want the speed of separation after 3 hours between two cars that started from the same point. One is moving at 16 mi/h south, the other is moving at 12 mi/h west.
Velocity vectors
Since both cars started from the same point, the speed of separation is the magnitude of the difference between the respective velocity vectors. A graphical representation of the velocity vectors shows them to be the legs of a right triangle. Their difference is the length of the hypotenuse, which can be found using the Pythagorean theorem.
s = √(16² +12²) = √(256 +144) = √400
s = 20
The speed of separation is a constant 20 mi/h.
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Additional comment
If the cars did not start at the same point, then the speed of separation would be changing with time. It could be found using the derivative of the distance between the cars, or by considering the car speeds in the direction each car is from the other at the time of interest.
We note that the problem here makes use of a 3-4-5 right triangle, with a multiplier of 4 mph.
