Final answer:
To find the fraction of the 24-hour period that elapses between 1:55 am and 8:05 pm, we calculate the elapsed time and express it as a fraction of 24 hours. The elapsed time in hours and minutes is 18 hours and 10 minutes, which simplifies to the fraction 19/24.
Step-by-step explanation:
The question asks what fractional part of a 24-hour period elapses between 1:55 am and 8:05 pm. To find the elapsed time, we need to calculate the time from 1:55 am to 8:05 pm.
Firstly, we convert the end time into the 24-hour format, so 8:05 pm becomes 20:05. Next, we calculate the hours elapsed from 1:55 am to 20:05. This is done by subtracting the start time from the end time. From 1:55 to 20:05, the elapsed time is 18 hours and 10 minutes. Since there are 24 hours in a day, we want to express this elapsed time as a fraction of a 24-hour period.
To convert 18 hours and 10 minutes to a fraction of a day, we first express the minutes as a fraction of an hour. There are 60 minutes in an hour, so 10 minutes is 10/60, or 1/6 of an hour. Therefore, the total elapsed time is 18 hours + 1/6 hour, which is the same as 18 1/6 hours. Now, express 18 1/6 hours as a fraction of 24 hours by dividing 18 1/6 by 24. This gives us the fraction 109/6 divided by 24, which simplifies to 109/144. The closest answer option to this fraction is 19/24 (Option F).