Answer: 1 hour and 60/11 minutes.
Step-by-step explanation:
How many degrees the Minute Hand Travels in 1 minute: 6º
How many degrees the Hour Hand Travels in 1 minute: 0.5º
If x is the number of minutes the clock traveled after 1 o'clock to reach the next meeting point,
The degrees that the minute hand traveled is 6 * x = 6xº
The degrees that the hour hand traveled is 0.5 * x = 0.5xº
In 12 hours the hour hand travels 360º,
So, in 1 hour, it travels 30º
Total number of degrees the clock traveled after 1 o'clock to reach the next meeting point,
6x = 30 + 0.5x
6x because the minute hand starts at the beginning.
30 because that counts for the number of degrees covered until 1 o'clock.
0.5x because that counts for the number of degrees the hour hand travels after 1 o'clock.
6x = 30 + 0.5x
5.5x = 30
55x = 300
x = 300/55 = 60/11
If you add back that one hour, then it becomes 1 hour and 60/11 minutes.