To find out how long it will take for the hands of a clock to form a 150° angle, given that they currently form a 60° angle, we can use the following method:
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Understand the movement of the clock hands: The minute hand moves at 360 degrees per hour (or 6 degrees per minute), and the hour hand moves at 30 degrees per hour (or 0.5 degrees per minute).
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Calculate the angular speed of the hands:
- The minute hand moves faster than the hour hand, so the rate at which the angle between them changes is: \[ \text{Rate} = \text{Speed of minute hand} - \text{Speed of hour hand} = 6° - 0.5° = 5.5° \text{ per minute} \]
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Current angle and target angle:
- Current angle = 60°
- Target angle = 150°
- Difference in angle = 150° - 60° = 90°
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Time to reach the target angle:
- Time (in minutes) to cover 90° at a rate of 5.5° per minute: \[ \text{Time} = \frac{90°}{5.5° \text{ per minute}} \approx 16.36 \text{ minutes} \]
Since we want the time in hours, we convert the minutes to hours: \[ \frac{16.36 \text{ minutes}}{60} \approx 0.2727 \text{ hours} \]
- Conclusion: Since 0.2727 hours is very close to approximately 0.27 hours, it indicates that Piper will go roller skating in less than half an hour from now.
Since the options provided are whole numbers of hours (3, 5, 7, and 9), the answer should be:
Piper will go roller skating in approximately 0 hours. Referring to the available choices, the closest time mentioned seems to be with an understanding that answer refers to significant time lapses only.
Please clarify how to prioritize absent options or avoid confusion if needed based on rising timelines like mentioned (indicating larger hours like 3, 5, 7 and 9). But numerically, Piper's set time for the activity doesn't extend to those multiple figures from the calculated angle progression hint.