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Calculus/Gr.12 Calculus - related rates

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Expert: - 2/28/2008


Question
A sports car and a transport leave a gas station at the same time. The sports car travels east at 150km/h while the transport travels north at the 80km/h. At what rate is the distance between the two vehicles increasing after 3 hours has passed?

I'm not sure what to do for this question. All I know is that the two cars make a right angle triangle. I tried using the pythagorean but it doesn't relate to how the rate increases after three hours. I would really appreciate any help you can give me.

Answer
It all comes down to applying the formula to find the length of the hypoteneuse c given sides a and b at right angles.

If is c=Sqrt(a^2+b^2).  Let c, a, and b all be functions of t.  Take the derivative (uses the chain rule,), and put in the values for a and b.  For da/dt, it's 150 and for db/dt, it's 80.

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