Time — Clock & Calendar • Topic 5 of 6

Elapsed Time

Elapsed time is the duration between a start and an end — End Time minus Start Time — and it is where base-60 regrouping really bites. There are three flavours of problem. To find the end time you add a duration to a start: add minutes to minutes and hours to hours, and if the minutes reach 60 or more, carry one hour. To find the start time you subtract backward, borrowing an hour as 60 minutes if the minutes you are taking away exceed those you have. To find the duration between two known times, you can subtract with borrowing — but the method recommended in primary classrooms is 'counting up'. Start at the earlier time, jump forward to the next whole hour, then by full hours, then by the leftover minutes, and add the jumps. For example, from 8:15 a.m. to 10:05 a.m.: 8:15 to 9:00 is 45 minutes, 9:00 to 10:00 is 1 hour, 10:00 to 10:05 is 5 minutes, giving 1 hour 50 minutes in total. Counting up avoids the borrowing that confuses children and mirrors how a clock actually advances. Two boundaries demand care: crossing noon (a.m. switches to p.m.) and crossing midnight (p.m. switches to a.m. and the date changes). When a span crosses midnight, split it — work out the time up to midnight, then the time after — and add the two pieces.

✅ Solved examples

1. A bus leaves at 9:30 a.m. and the journey takes 2 hours 45 minutes. What time does it arrive?
Add in steps. 9:30 + 2 hours = 11:30 a.m. Then 11:30 + 30 minutes = 12:00 noon. Then + 15 minutes = 12:15 p.m. The bus arrives at 12:15 p.m.
2. Find the elapsed time from 8:15 a.m. to 10:05 a.m. using the counting-up method.
8:15 to 9:00 = 45 minutes; 9:00 to 10:00 = 1 hour; 10:00 to 10:05 = 5 minutes. Total = 1 hour + 45 min + 5 min = 1 hour 50 minutes.
3. A film ends at 4:15 p.m. and ran for 2 hours 50 minutes. What time did it start?
Subtract backward. 4:15 - 2 hours = 2:15 p.m. Now take 50 minutes from 2:15: borrow 1 hour, so 2:15 = 1 hour and 75 minutes; 75 - 50 = 25 minutes, leaving 1:25 p.m. The film started at 1:25 p.m.
4. A night train runs from 9:30 p.m. on Monday to 3:15 a.m. on Tuesday. How long is the journey?
Split at midnight. From 9:30 p.m. to 12:00 midnight = 2 hours 30 minutes. From 12:00 a.m. to 3:15 a.m. = 3 hours 15 minutes. Total = 5 hours 45 minutes.

✏️ Practice — try these, take hints as needed

1. A class starts at 10:20 a.m. and lasts 40 minutes. When does it end?
Add 40 minutes to 20 minutes.
The minutes reach 60, so carry one hour.
11:00 a.m.
2. How much time passes from 6:45 p.m. to 8:10 p.m.?
Count up to 7:00 first (15 min).
Then 7:00 to 8:00, then to 8:10.
1 hour 25 minutes
3. A meeting finished at 1:10 p.m. after running for 1 hour 25 minutes. When did it start?
Subtract backward and borrow an hour.
1:10 = 12 hours 70 minutes.
11:45 a.m.
4. A guard works from 10:30 p.m. to 2:00 a.m. How long is the shift?
Cross midnight, so split the span.
10:30 p.m. to midnight, then midnight to 2:00.
3 hours 30 minutes

📝 Topic test — 8 questions

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