Final answer:
Using equations to represent the conditions given, the time 10 minutes after Raccoon Pyotr first looks at the clock shows that it is 6:05.
Step-by-step explanation:
The question involves solving a problem related to reading analog clocks and understanding the relationship between the positions of the hour and minute hands. To solve the problem, let's use two equations. In the first instance, according to Raccoon Pyotr, the minute hand is showing 11 times more minutes than the hour hand is showing hours.
If we let x represent the number of hours and 11x represent the number of minutes, our first equation is 60x + 11x = (minutes after the hour) for the minute hand. In the second instance, 10 minutes later, the minute hand shows 1 minute less than the hour hand shows hours, which gives us the equation 60(x + 1/6) - 1 = (hours), where x + 1/6 accounts for the additional 10 minutes ((1/6) of an hour).
By simultaneously solving these two equations, we find that the first instance occurs at 5:55 (where x = 5 and the minutes = 5 * 11 = 55), and then 10 minutes later it will be 6:05 (5 hours and 65 minutes, but 60 minutes make an hour so we add 1 to hours and subtract 60 from minutes).