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# Word Problems/algebra

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

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

Word Problems

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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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