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Neela's clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o'clock position. Suppose Neelas first looks at the clock when the hands are aligned and it shows 3:15. She looks at the clock again and sees that the hour and minute hands of the clock form the arms of an angle measuring- 105 degrees through which of the following could the minute hand have rotated to reach its current position?

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Final answer:

When the minute hand has rotated to form a 105-degree angle with the hour hand fixed at 3 o'clock, it has moved 3.5 hours indicating a time around 6:45 or 18:45. This is a mathematical geometry problem involving angle measurements and clock hand positions.

Step-by-step explanation:

The problem at hand involves understanding the movement of clock hands and relating it to angle measurement, which falls under the subject of Mathematics, specifically dealing with geometry and the concept of angles. As Neela's clock is broken with the hour hand stuck at the three o'clock position, we are only considering the motion of the minute hand and its angular displacement relative to this fixed hour hand. When the student looks at the clock for the first time and sees the hands aligned at 3:15, the minute hand is at the quarter hour mark, i.e., at 3 on the dial.

Keeping in mind that the hour hand is immobile and fixed at 3 o'clock, if the minute hand now forms a 105-degree angle with the hour hand, we must calculate the rotation of the minute hand. A 105-degree angle formed can be the result of the minute hand moving clockwise from 3:15 to somewhere between 4 and 5. Since it makes a complete rotation every hour (360 degrees), we divide 105 by 30 degrees (since 360 degrees/12 hours = 30 degrees/hour) to find that it has moved 3.5 hours from 3:15. This calculation suggests that the time indicated by the minute hand would be approximately 6:45 or 18:45 (6:45 PM), as the minute hand would have rotated 3.5 hours worth of minute tick marks on the clock face from the initial 3:15 position.

Practice problems such as these help students understand the relationship between time and angle in analog clocks, fostering their geometric reasoning skills.

User Awin
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4 votes
The answer would be 3:55 :D hope this helped!!!
User Thierry Templier
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6.2k points