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## Related Rates

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### Related Rates

Right away, you can tell if a given problem is a related rates problem because it will contain wording like "HOW QUICKLY IS...CHANGING?" Related rates problems help you figure out how fast one variable is changing if you know exactly how quickly another variable is changing. No two problems are exactly alike, but the procedure is the same for all problems of this type.

Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 2 ft/sec. How fast is the area of the spill increasing at the instant when the radius of the spill is 60 feet?

given: $\frac{dr}{dt}=2$

find: $\frac{dA}{dt}$ when r = 60 ft

A = πr2

$\frac{dA}{dt}$ = 2πr$\frac{dr}{dt}$

= 2π(60)(2)
= 240π ft2/sec

The area of the spill is increasing at 240π ft2/sec.
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