A clock is set right at 10PM. the clock gains 10 minutes i 24 hours. What will be the true time when the clock indicates 3PM the following day.
Clock runs 10 minutes fast every 24 (real) hours.
So clock shows 24*60+10=1450 minutes after 1440 minutes.
3PM-10PM=2+15 hours = 17 hours = 1020 minutes.
Actual time passed from 10PM
= 10pm + 1020*(144/145)
=10 pm + 1012 28/29 minutes
=14:52:57.93
To determine the true time when the clock indicates 3PM the following day, we need to calculate the time gained by the clock in 24 hours and then add that to the indication of the clock.
First, let's calculate the time gained in one hour. The clock gains 10 minutes in 24 hours, so in one hour, it will gain (10 minutes / 24 hours) = 10/24 minutes = 5/12 minutes.
Next, we can find the time gained from 10PM to 3PM, which is 5 hours. Therefore, the clock will gain (5/12 minutes per hour) * 5 hours = 25/12 minutes in total.
Now, let's add the gained time to the clock's indication of 3PM. The clock's indication of 3PM plus the gained time of 25/12 minutes will give us the true time.
To add the time, we convert 3PM to minutes. Since 1 hour is equal to 60 minutes, 3 hours will be equal to (3 hours * 60 minutes/hour) = 180 minutes.
Finally, we add the gained time of 25/12 minutes to 180 minutes:
Total time = 180 minutes + 25/12 minutes
To simplify the calculation we can convert the improper fraction 25/12 to a mixed number:
25/12 = 2 1/12
Total time = 180 minutes + 2 1/12 minutes
Adding the mixed number:
Total time = 180 minutes + 2 1/12 minutes = 180 minutes + 25/12 minutes = (180*12 + 25) /12 minutes = 2175/12 minutes
To convert this fraction into hours and minutes, we divide the numerator (2175) by the denominator (12) and obtain the quotient and remainder:
2175 รท 12 = 181 with a remainder of 3
Thus, the true time when the clock indicates 3PM the following day is 181 hours and 3 minutes.
Note: Since a day has 24 hours, we need to convert the extra hours into days. 181 hours is equal to 7 days and 13 hours. Therefore, the true time will be 7 days and 13 hours plus the 3 extra minutes after 3PM.