# Word Problems/Derivatives

Question
What is the answer to this word problem? Trigonometry can be used to assist in getting the answer, but derivatives or differentiation must be used.

A 20 foot ladder is leaning against a house when its base starts to slide away. By the time the base is 12 feet from the house, the base is moving at 2 feet/second? How fast is the ladder sliding down the wall at that moment?

By the Pythagorean Theorem,
y² = 20²-x²
When x = 12 ft:
the horizontal rate of change is dx/dt = 2 feet per second.
y = 16 ft

Differentiate y² with respect to time.
dy²/dt = 0 - dx²/dt
2y·dy/dt = -2x·dx/dt
dy/dt = (-x/y)·dx/dt

x=12, y=16, dx/dt=2 ft/sec:
dy/dx = (-12/16)·2 = -1.5
The ladder slides down the wall at 1.5 feet per second.
Questioner's Rating
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Word Problems

Volunteer

#### Janet Yang

##### Expertise

Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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