7. A watch that loses a half-minute every hour was set to read the correct time at 05 45h on Monday. Determiner the time, in the 12-hour system, the watch will show on the following Friday at 19 45h.
Elapsed time=5 days and 14 hours=134 hous
Lost time = 134*0.5 min.=67 minutes
19:45-67 min. = 18:38 = 6:38 am.
To determine the time the watch will show on the following Friday at 19:45 in the 12-hour system, we need to calculate the number of hours that will pass from Monday 05:45 to Friday 19:45.
Let's break it down step-by-step:
Step 1:
The watch loses half a minute every hour. So, in 24 hours, it will lose 24 * 0.5 = 12 minutes.
Step 2:
From Monday 05:45 to Friday 05:45, there are 4 days. Since each day is 24 hours, we have a total of 4 * 24 = 96 hours.
Step 3:
The watch will lose 12 minutes per hour for 96 hours, which means it will lose 12 * 96 = 1,152 minutes.
Step 4:
Since 60 minutes make up 1 hour, we can convert the lost minutes to hours by dividing 1,152 by 60. That gives us 1,152 / 60 = 19.2 hours.
Step 5:
Now, we add the 19.2 hours lost to the original time of 05:45 on Monday, which gives us 05:45 + 19:12 (rounding up) = 24:57 (24-hour system).
Step 6:
Converting the 24-hour time to the 12-hour system, we subtract 12 from the hours if it is greater than 12. In this case, 24:57 becomes 24 - 12 = 12:57 PM.
Therefore, the watch will show 12:57 PM on the following Friday at 19:45 in the 12-hour system.
To determine the time the watch will show on the following Friday at 19:45, we need to calculate the number of hours that have passed between Monday at 5:45 and Friday at 19:45.
First, let's calculate the number of hours between Monday 5:45 and Friday 19:45:
- Monday 5:45 to Tuesday 5:45: 24 hours
- Tuesday 5:45 to Wednesday 5:45: 24 hours
- Wednesday 5:45 to Thursday 5:45: 24 hours
- Thursday 5:45 to Friday 5:45: 24 hours
- Friday 5:45 to Friday 19:45: 14 hours
So, from Monday 5:45 to Friday 19:45, a total of 24 + 24 + 24 + 24 + 14 = 110 hours have passed.
Now, we know that the watch loses half a minute every hour. Therefore, for every hour that passes, the watch will show 59.5 minutes.
Let's calculate the number of minutes shown on the watch from Monday 5:45 to Friday 19:45:
110 hours x 59.5 minutes = 6545 minutes
To convert 6545 minutes into hours and minutes, we divide by 60:
6545 minutes / 60 = 109 hours and 5 minutes
Now, we add the 109 hours and 5 minutes to the starting time of Monday 5:45:
5:45 + 109 hours = 114:45
Since we are using the 12-hour system, we need to convert 114:45 to the correct format.
114 divided by 12 is 9 with a remainder of 6. So, there are 9 full 12-hour cycles in 114, and the watch will show the correct time after completing these cycles.
The remainder of 6 indicates that the watch will show 6 hours past 12:00.
Therefore, the watch will show 6:45 in the 12-hour system on the following Friday at 19:45.