The hands of a clock are 10 cm and 7 cm long, respectively. Find the difference in the distance traversed by their tips in **3 days and 5 hours**.

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To calculate the difference in the distances traversed by the tips of the minute and hour hands, we first determine the number of rotations completed by each hand in **3 days and 5 hours**.

1. **Number of rounds completed by the minute hand:**  
The minute hand completes one full round every hour. In **3 days (72 hours) and 5 hours**, the total number of rounds is:  
$$
	ext{Minute hand rounds} = (3 	imes 24 + 5) = 77.
$$

2. **Number of rounds completed by the hour hand:**  
The hour hand completes one full round every 12 hours. In **3 days (72 hours) and 5 hours**, the total number of rounds is:  
$$
	ext{Hour hand rounds} = \left( \frac{3 	imes 24}{12} + \frac{5}{12} ight) = 6 \frac{5}{12}.
$$

3. **Distance traversed by each hand in one round:**  
The distance traversed is equal to the circumference of the circle traced by each hand:  
- For the minute hand (length = 10 cm): $$ C_m = 2 \pi r = 2 	imes \frac{22}{7} 	imes 10 = \frac{440}{7} \, 	ext{cm}. $$  
- For the hour hand (length = 7 cm): $$ C_h = 2 \pi r = 2 	imes \frac{22}{7} 	imes 7 = 44 \, 	ext{cm}. $$

4. **Total distance traversed by each hand:**  
- Minute hand:  
$$
	ext{Distance by minute hand} = 77 	imes C_m = 77 	imes \frac{440}{7} = 4840 \, 	ext{cm}.
$$  
- Hour hand:  
$$
	ext{Distance by hour hand} = (6 + \frac{5}{12}) 	imes C_h = (6 + 0.4167) 	imes 44 = 6.4167 	imes 44 = 282.33 \, 	ext{cm}.
$$

5. **Difference between distances traversed:**  
The difference is:  
$$
	ext{Difference} = 4840 - 282.33 = 4557.67 \, 	ext{cm}.
$$

Thus, the difference in distances traversed by their tips is **4557.67 cm**.

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