Word Problems/algebra

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Question
in how many minutes after four o'clock will the minute hand coincides with the hour hand ?

Answer
Measure angles with respect to the positive y-axis, increasing in the clockwise direction.

At four o'clock, the angle of the minute hand is 0.
The minute hand travels 2π radians per hour = π/30 radian per minute.
At t minutes after four o'clock, the angle of the minute hand is tπ/30.

At four o'clock, the angle of the hour hand is 2π/3.
The hour hand travels 2π/12 radian per hour = π/360 radian per minute.
At t minutes after four o'clock, the angle of the hour hand is (2π/3) + (tπ/360).

Solve for t:
tπ/30 = (2π/3) + (tπ/360)
12tπ/360 = 240π/360 + tπ/360
12tπ = 240π + tπ
12t = 240 + t
11t = 240
t = 240/11≅ 21.8 minutes

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Janet Yang

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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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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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