MHB Algebra word problem: the angle between the hands of a clock

AI Thread Summary
The discussion focuses on determining the specific time between 2 and 3 o'clock when the angle formed by the clock's hands is bisected by a line from the center to the 3 o'clock mark. The key unknown in this problem is the number of minutes after 2 o'clock, denoted as x. Participants seek clarification on how to rephrase the question for better understanding. The problem involves calculating the angle between the hour and minute hands at a given time. Understanding this concept is essential for solving the algebraic word problem effectively.
bergausstein
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1. What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?

can you rephrase for me the question. what's the unknown here? please help thanks!
 
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Re: Algebra word problem.

bergausstein said:
1. What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?

can you rephrase for me the question. what's the unknown here? please help thanks!

View attachment 1661

The unknown is the number of minutes x after 2 o'clock.
 

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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