Answer :
The true time when the clock indicates 3 p.m. is actually 3:00 p.m.
To solve this problem, we first need to determine how much time passes on the clock from 11 a.m. to 3 p.m. and then adjust for the gained time according to the clock's error rate.
From 11 a.m. to 3 p.m., 4 hours pass. According to the clock, this will be 4 hours on display.
Now, let's calculate the rate at which the clock gains time. The clock gains 12 minutes in 12 hours. To find the gain per hour, we divide the gain in minutes by the number of hours:
Gain per hour = Total gain in minutes / Total hours
Gain per hour = 12 minutes / 12 hours
Gain per hour = 1 minute per hour
This means the clock gains 1 minute every hour. Since 4 hours have passed on the clock from 11 a.m. to 3 p.m., the clock will have gained an additional:
4 hours × 1 minute per hour = 4 minutes
So, when the faulty clock shows 3 p.m., it will have gained an extra 4 minutes, indicating the time as 3:04 p.m. according to the clock.
To correct this to find the true time, we need to subtract the gained minutes from the indicated time:
Indicated time = 3:04 p.m.
Gained time = 4 minutes
True time = Indicated time - Gained time
True time = 3:04 p.m. - 4 minutes
True time = 3:00 p.m.
Hence, the true time when the clock indicates 3 p.m. is actually 3:00 p.m.
