From the start to the end
A film starts at 3:40pm and ends at 4:10pm. How long does it last? The length of time from the start to the end is called the duration.
The start and the end are in different hours, so the minutes cannot just be taken away from each other: 10 − 40 does not make sense. Count up from the start time instead.
The film starts at 3:40pm and ends at 4:10pm. The line between the two clocks is the time it lasts.
Count up to the hour, then past it
First count up to the next o’clock. An hour is 60 minutes, so from 3:40 to 4:00 is 60 − 40 = 20 minutes.
Then carry on from 4:00 to the end. From 4:00 to 4:10 is 10 minutes. Add the two parts: 20 + 10 = 30, so the film lasts 30 minutes.
20 minutes reach 4:00pm, and 10 more reach 4:10pm: 30 minutes in all.
3:40 = 40 minutes past 3: the long hand counts the minutes, and the short hand has moved on from 3 toward 4
Set the clock to 4:10
Turn the long hand from 3:40 to 4:10. It passes 4 numbers on the way to the 12, which is 20 minutes and the start of a new hour, and then 2 numbers more, which is 10 minutes.
Durations longer than an hour
The same counting works when more than one hour goes by. From 2:35pm to 5:10pm, 25 minutes reach 3:00pm, then 2 hours reach 5:00pm, and 10 more minutes reach 5:10pm. The minutes add to 25 + 10 = 35, so the duration is 2 hours 35 minutes.
Finding the end or the start
Counting up also finds when something ends. A class starts at 9:50am and lasts 40 minutes. The first 10 minutes reach 10:00am, which leaves 40 − 10 = 30 minutes, so the class ends at 10:30am.
To find when something started, count back from the end. A film ends at 11:15pm after 35 minutes. Counting back 15 minutes reaches 11:00pm, and the other 20 minutes go back to 10:40pm, so the film started at 10:40pm.
The class starts at 9:50am: 10 minutes reach 10:00am, and the other 30 end it at 10:30am.
An hour is 60 minutes, not 100
The usual mistake treats the times as ordinary numbers. Working out 410 − 340 = 70 gives 70 minutes for the film, but that subtraction borrows 100 from the hours, and an hour holds only 60 minutes. The film lasts 30 minutes.
The other slip stops at the hour. 20 minutes reach 4:00pm, but the film goes on until 4:10pm, so the 10 minutes after 4:00pm still have to be added.
Worked example: A Journey in Two Legs with a Rest, Crossing Noon
Question A bus leaves the school at 10.45 a.m. It travels for 1 h 35 min, stops for a rest of 25 min, and then travels for another 50 min to reach the camp. (a) At what time does the bus reach the camp? (b) What is the total traveling time, not counting the rest?
1.Add the first leg to the starting time. One hour after 10.45 a.m. is 11.45 a.m. Of the 35 min, 15 min reaches 12 noon and the other 20 min reaches 12.20 p.m.
From 10.45 a.m., 1 h reaches 11.45 a.m., 15 min more reaches 12 noon, and the last 20 min reaches 12.20 p.m. 2.Add the rest of 25 min: 12.20 p.m. becomes 12.45 p.m.
The rest of 25 min ends at 12.45 p.m. 3.Add the second leg of 50 min. The first 15 min reaches 1.00 p.m. and the other 35 min reaches 1.35 p.m.
(a) From 12.45 p.m., 15 min reaches 1.00 p.m. and the other 35 min reaches 1.35 p.m. 4.(a) The bus reaches the camp at 1.35 p.m.
5.(b) The rest is not traveling time. The two legs take 1 h 35 min + 50 min = 1 h 85 min = 2 h 25 min. Check: from 10.45 a.m. to 1.35 p.m. is 2 h 50 min, and 2 h 50 min − 25 min = 2 h 25 min.
(b) Only the two gold blocks are traveling time: 2 h 25 min.
Answer: (a) 1.35 p.m.; (b) 2 h 25 min, which is 145 min
Common mistakes
- Adding the times as decimals: 10.45 + 1.35 = 11.80. There are 60 minutes in an hour, not 100, so 45 min + 35 min = 80 min is 1 h 20 min.
- Giving 2 h 50 min as the traveling time. That is the whole time from leaving to arriving, and it includes the rest of 25 min when the bus was not moving.