Chapter 3 Section 11

# Chapter 3 Section 11 - 3.11 Related Rate Word Problems page...

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3.11 Related Rate Word Problems page 199

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Objectives Set up and solve related rates word problems.
If we are pumping air into a balloon, both the volume and the radius of the balloon are increasing and their rates of increase are related to each other. But it is much easier to measure directly the rate of increase of the volume than the rate of increase of the radius. In a related rates problem the idea is to compute the rate of change of one quantity in terms of the rate of change of another quantity (which may be more easily measured). The procedure is to find an equation that relates the two quantities and then use the Chain Rule to differentiate both sides with respect to time.

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Example: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?
10 ft 6 ft dx/dt = 1 ft/s s ft dt dy dt dx y x dt dy dt dy y dt dx x y x y x z y x / 4 3 ) 1 ( 8 6 0 2 2 100 ) 10 ( 2 2 2 2 2 2 2 2 - = - = - = = + = + = + = +

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Chapter 3 Section 11 - 3.11 Related Rate Word Problems page...

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