How many times both hands of clock are at 0° angle between Monday 7:00 am to Tuesday 9:00 pm ?

To determine how many times the hands of a clock are at a \(0^\circ\) angle (overlap) between **Monday 7:00 am** and **Tuesday 9:00 pm**, we can break the problem into manageable steps.

### Key Observations:
- The hands of a clock overlap every **12/11 hours**.
- In a full 12-hour period, the hands overlap **11 times**.

### Time Span:
1. From **Monday 7:00 am** to **Tuesday 9:00 pm**, we have 38 hours:
   - From **Monday 7:00 am** to **Monday 7:00 pm**: 12 hours.
   - From **Monday 7:00 pm** to **Tuesday 7:00 pm**: 24 hours.
   - From **Tuesday 7:00 pm** to **Tuesday 9:00 pm**: 2 hours.
   
   So, total hours = \(12 + 24 + 2 = 38\) hours.

### Calculation:
- In a 12-hour period, there are **11 overlaps**.
- In a 24-hour period (full day), there are **22 overlaps**.
- For the 2 additional hours on Tuesday, there is **1 overlap**, because overlaps occur approximately every **1 hour and 5 minutes** (\(12/11 \approx 1.09\)).

### Total Overlaps:
- From Monday 7:00 am to Tuesday 7:00 pm (36 hours): \(33\) overlaps (since \(11 \times 3 = 33\)).
- Plus 1 overlap between Tuesday 7:00 pm and Tuesday 9:00 pm.

So, the total number of overlaps is \(33 + 1 = 34\).

### Final Answer:
The hands of the clock overlap **34 times** between Monday 7:00 am and Tuesday 9:00 pm.

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Would you like to dive into more details about the process? Here are some related questions:

1. How do we calculate when the hands of a clock form a 180° angle?
2. Can the overlap times be predicted for any given hour?
3. How does the clock angle formula work for other angles?
4. What is the derivation for the formula \(12/11\) hours for overlap?
5. How does the time between overlaps change if the clock speed is altered?

**Tip**: The \(12/11\) hour interval comes from the fact that the minute hand moves 12 times faster than the hour hand, and they meet roughly every 65.45 minutes.

How many times both hands of clock are at 0° angle between Monday 7:00 am to Tuesday 9:00 pm?

Find out how many times the hands of a clock overlap at 0° between Monday 7:00 AM and Tuesday 9:00 PM. This solution explains the clock overlap formula, using key concepts such as time intervals and the relative speed of clock hands. Ideal for students in Grades 7-10.

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