At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?54 (6/11) min past 5.55 (6/11) min past 4.56 (6/11) min past 4.54 (6/11) min past 4.

The hands of a watch point in opposite directions at 54 (6/11) minutes past 4.

Here's the step by step explanation:

1. We know that the minute hand moves 12 times faster than the hour hand.

2. At 4 o'clock, the hour hand is at 4 and the minute hand is at 12. They are 20 minute spaces apart (since each hour represents 5 minute spaces).

3. We want them to be 30 minute spaces apart for them to be in opposite directions (180 degrees apart).

4. So, the minute hand needs to move 10 more minute spaces than the hour hand.

5. Since the minute hand moves 12 times faster than the hour hand, it will take 60/(12-1) = 60/11 = 5 (5/11) minutes for the minute hand to gain 1 minute space on the hour hand.

6. Therefore, it will take 10 * 5 (5/11) = 54 (6/11) minutes for the minute hand to gain 10 minute spaces on the hour hand.

7. So, the hands of a watch will point in opposite directions at 54 (6/11) minutes past 4.