Math Problem Statement

The grandfather clock at the top of the stairs says it is now 3:20AM. In how many minutes from now will the hour and minute hand of the clock first meet each other? Please round to the nearest minute. Include just the number and no other text.

Solution

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Math Problem Analysis

Mathematical Concepts

Clock Angles
Relative Motion

Formulas

Angle between hour and minute hand = |30 * hour - 5.5 * minutes|
Relative speed of minute hand to hour hand = 5.5 degrees per minute

Theorems

The hour and minute hands meet when their relative positions align over time

Suitable Grade Level

Grades 10-12

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