Given conditions:

• The time is between 8:00 and 9:00.
• The hour and minute hands coincide (one above the other).
• We need to find when they will coincide again.

Step 1: Finding the first coincidence At 8:00, the hour hand is at $8 \times 30 = 240^\circ$. The minute hand starts at 0° and moves 360° per hour (6° per minute). The hour hand moves 30° per hour (0.5° per minute).

Let $t$ be the time in minutes after 8:00 when they coincide: $240 + 0.5t = 6t$ $240 = 5.5t$

$t = 240 / 5.5 = 43.64$

Step 2: Finding the next coincidence The hands coincide every $360^\circ / (5.5^\circ \text{ per minute}) \approx 65.45 \text{ minutes}$.

Rounding to the nearest integer: $65 \text{ minutes}$.