At what time between 8 and 9 o'clock do the hands of a clock coincide?

Question

Accepted Answer

1. **Formula Used:**  
   The angle between the hour hand and the minute hand is given by:  
   $$
   	heta = |30H - \frac{11}{2}M|
   $$  
   For the hands to coincide, the angle ($$	heta$$) must be $$0^\circ$$.

2. **Substitute values into the formula:**  
   - At 8 o'clock, $$H = 8$$.  
   - Set $$	heta = 0$$:  
     $$
     0 = |30(8) - \frac{11}{2}M|
     $$

3. **Simplify the equation:**  
   $$
   240 = \frac{11}{2}M
   $$

4. **Solve for $$M$$:**  
   Multiply through by $$2$$:  
   $$
   M = \frac{480}{11} = 43 \frac{7}{11}
   $$

5. **Interpret the result:**  
   The hands of the clock coincide at $$43 \frac{7}{11}$$ minutes past 8.

Thus, the correct answer is **(b)** $$43 \frac{7}{11}$$ min past 8.

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