Time — Class 5 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 5 Mathematics, Unit 5. Railway time, normal time and railway time, and finding time intervals. Taught in August.
1. Two ways of telling the time
The clock on your wall shows the numbers 1 to 12, so it goes round twice in a day. Eight o'clock happens in the morning and again in the evening, which is why we add a.m. for the first half of the day and p.m. for the second.
That works in conversation but not on a timetable. A train leaving at "8:00" could be one of two trains twelve hours apart.
So the railways use a 24-hour clock, called railway time. The hours run straight through from 00 to 23, and there is no a.m. or p.m. at all.
Railway time is used at railway stations, in the defence services, and on television and the internet.
2. Converting normal time into railway time
Morning times (a.m.) keep the same hour, written with two digits.
- 3:30 a.m. becomes 03:30 hours
- 9:40 a.m. becomes 09:40 hours
Afternoon and evening times (p.m.) add 12 to the hour.
- 4:15 p.m. becomes 16:15 hours
- 1:55 p.m. becomes 13:55 hours
Two special cases, and these are the ones that catch people out:
- 12 noon stays 12:00 hours. Do not add 12 and do not make it 00:00.
- 12 midnight becomes 00:00 hours.
So 12:25 p.m., being just after noon, is simply 12:25 hours.
3. Converting railway time back to normal time
If the hour is less than 12, it is a morning time; write it with a.m.
If the hour is more than 12, subtract 12 and write p.m.
- 12:50 hours is 12:50 p.m.
- 20:15 hours: 20 − 12 = 8, so 8:15 p.m.
- 23:40 hours: 23 − 12 = 11, so 11:40 p.m.
| Normal time | Railway time |
|---|---|
| 3:30 a.m. | 03:30 hours |
| 9:40 a.m. | 09:40 hours |
| 12:25 p.m. | 12:25 hours |
| 1:55 p.m. | 13:55 hours |
| 4:15 p.m. | 16:15 hours |
| 8:15 p.m. | 20:15 hours |
| 11:40 p.m. | 23:40 hours |
4. Adding time
Write hours under hours and minutes under minutes. Add each column — then remember that an hour has 60 minutes, not 100. If the minutes reach 60 or more, convert.
Add 4 hours 30 minutes and 2 hours 45 minutes:
| Hours | Minutes | |
|---|---|---|
| 4 | 30 | |
| + | 2 | 45 |
| 6 | 75 |
75 minutes is 1 hour 15 minutes, so carry the hour: 6 + 1 = 7.
The answer is 7 hours 15 minutes.
5. Subtracting time, and finding a duration
The duration is how long something lasts: the end time minus the start time.
When the minutes at the top are too small, borrow 1 hour as 60 minutes.
Ram works at his computer from 10 o'clock in the morning until 3:30 in the evening. How long does he work?
Write the finishing time as 3:30 p.m., which is 15:30 in railway time, and the start as 10:00.
| Hours | Minutes | |
|---|---|---|
| Finish | 15 | 30 |
| Start | − 10 | 00 |
| 5 | 30 |
Ram works for 5 hours 30 minutes.
Converting to railway time first is the safest habit for any duration that crosses midday.
6. Reading a school timetable
| Event | Time |
|---|---|
| First bell | 9:00 a.m. |
| Morning prayer | 9:15 a.m. |
| Class starting time | 9:30 a.m. |
| Morning break | 11:00 a.m. to 11:10 a.m. |
| Morning school closes | 12:40 p.m. |
| Lunch | 12:40 p.m. to 2:00 p.m. |
| Afternoon school starts | 2:00 p.m. |
Morning working time runs from 9:30 a.m. to 12:40 p.m. Subtracting: the minutes need a borrow, so 100 − 30 = 40 minutes and 11 − 9 = 2 hours. That is 3 hours 10 minutes.
7. Worked examples
Example 1. Write 3:30 a.m. in railway time.
Solution: Morning times keep the hour: 03:30 hours.
Example 2. Write 4:15 p.m. in railway time.
Solution: Add 12 to the hour: 16:15 hours.
Example 3. Write 20:15 hours in normal time.
Solution: 20 − 12 = 8, so 8:15 p.m.
Example 4. Write 12:25 p.m. in railway time.
Solution: 12:25 hours. Noon keeps its hour.
Example 5. Add 3 hours 50 minutes and 2 hours 40 minutes.
Solution: 50 + 40 = 90 minutes = 1 hour 30 minutes. Hours: 3 + 2 + 1 = 6. Answer 6 hours 30 minutes.
Example 6. Subtract 1 hour 20 minutes from 4 hours 25 minutes.
Solution: 25 − 20 = 5 minutes and 4 − 1 = 3 hours. Answer 3 hours 5 minutes.
Example 7. Subtract 3 hours 55 minutes from 5 hours 45 minutes.
Solution: 45 is less than 55, so borrow an hour: 105 − 55 = 50 minutes, and 4 − 3 = 1 hour. Answer 1 hour 50 minutes.
Example 8. A school works from 9:30 a.m. to 4:00 p.m. Find the working duration.
Solution: 4:00 p.m. is 16:00. Then 16:00 − 9:30: borrow an hour, so 60 − 30 = 30 minutes and 15 − 9 = 6 hours. Answer 6 hours 30 minutes.
8. Practice
- Why does the railway use a 24-hour clock?
- Write 9:40 a.m. in railway time.
- Write 11:15 p.m. in railway time.
- Write 23:40 hours in normal time.
- What is 12 noon in railway time?
- Add 5 hours 35 minutes and 1 hour 40 minutes.
- Subtract 2 hours 20 minutes from 6 hours 55 minutes.
- An office works from 10 a.m. to 6 p.m. Find the duration.
- A film begins at 14:45 hours and runs for 2 hours 30 minutes. When does it end?
9. Answers
- Because an ordinary clock shows every hour twice a day, so a.m. and p.m. could be confused on a timetable. Numbering the hours 00 to 23 removes any doubt.
- 09:40 hours.
- 23:15 hours.
- 23 − 12 = 11, so 11:40 p.m.
- 12:00 hours. Only midnight becomes 00:00.
- 35 + 40 = 75 minutes = 1 hour 15 minutes, so 5 + 1 + 1 = 7 hours 15 minutes.
- 55 − 20 = 35 minutes and 6 − 2 = 4 hours, giving 4 hours 35 minutes.
- 6 p.m. is 18:00, so 18:00 − 10:00 = 8 hours.
- 14:45 + 2 hours = 16:45, plus 30 minutes = 17:15 hours, which is 5:15 p.m.
10. Summary
- An ordinary clock runs twice a day, so it needs a.m. and p.m.
- Railway time uses a 24-hour clock, 00 to 23, with no a.m. or p.m.
- It is used at railway stations, in the defence services, and on television and the internet.
- Morning times keep their hour; afternoon and evening times add 12.
- 12 noon stays 12:00 hours; 12 midnight becomes 00:00 hours.
- To read railway time back, subtract 12 from any hour greater than 12 and write p.m.
- Add and subtract in hour and minute columns, remembering 60 minutes to an hour.
- Carry an hour when the minutes reach 60; borrow an hour as 60 minutes when they are too small.
- Duration = end time − start time; convert to railway time first when the period crosses midday.
