Calculus homework question

Question

Two cars leave from the same location at exactly 8:00am if cat A is driving directly north at 60 miles per hour and car B is driving directly east at 25 miles per hour determine the rate that the distance between the cars is changing at 10:00am

Answer 1

At moment t distance d between cars d² = (60t)² + (25t)²= 4225t².

So, d = 65t. Then rate of change of distance is derivative d' = 65 mi/h is constant. And because at 10:00 AM d' = 65 mi/h

Answer 2

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| a= 60 mph North

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L__________> b= 25 mph East

If you're going to look at the figure above, the rate that we are looking for is the hypotenuse of a right triangle. From 8am to 10am is 2 hours.

So let say:

c = rate of the distance between the car is changing.

Using the Pythagorean Theorem.

c² = a²+b²

c² = (60)²+(25)²

c =√(3600+625)

c = 65 miles per hour.

The 2 hours doesn't matter because the rate is still going to be the same in any time. However, if you are looking for the distance after 2 hours, that would be (65)(2) = 130 miles.

65 miles per hour is basically the same as 130 miles in 2 hours.