Time Problems
Every question with a fully worked solution.
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Theory
A time problem is solved in steps. Find what you know (a start time, a finish time or a duration), draw a time line, then count on or count back. This Year 7 maths page shows finish times, latest start times, pay, parking, events with gaps, ages in years and months, and trips across a time zone.
How long? Count on in easy jumps from the start time: to the next o’clock, then whole hours, then the minutes left.
Finish time \(=\) start time \(+\) duration. Add the hours first, then the minutes through the next o’clock: 3:50 pm \(+ 2\) h \(25\) min: 5:50 pm, then 6:00 pm, then 6:15 pm.
Start time \(=\) finish time \(-\) duration. To find the latest time to start, begin at the deadline and count back each step.
Two clock faces. Read each clock and write both times first, then count on from the start time.
Check by adding all the parts and counting on again to the answer.
Types of time problem:
| Problem type | What to do | For example |
|---|---|---|
| A trip in several parts | Add each part in order. | \(12 + 9 + 47\) min \(= 68\) min \(= 1\) h \(8\) min |
| Repeated events | \(n\) events have \(n - 1\) gaps between them. | \(6\) races of \(10\) min with \(2\)-min gaps: \(6 \times 10 + 5 \times 2 = 70\) min |
| Pay per hour | Change minutes to a decimal of an hour; pay = hours × rate. | \(7\) h \(45\) min \(= 7.75\) h |
| Each hour or part of an hour | Every started hour is charged. | \(2\) h \(5\) min is charged as \(3\) h |
| Years and months | Years first, then months one at a time, past January. | June 2020 \(-\) \(5\) years \(8\) months \(=\) October 2014 |
| Across a time zone | Change both times to the same zone first. | a zone \(2\) h behind: take \(2\) h off its times |
How to solve a time problem
- Write what you know: start, finish or duration.
- Draw a time line and count on (or back) in easy jumps.
- Change to one time zone, or to decimal hours for pay, if needed.
- Check by counting on from the start to the answer.
| \(20 + 25\) | \(=\) | \(45\) |
10:40 am \(+ 1\) h \(=\) 11:40 am, \(+ 20\) min \(=\) 12:00 pm, \(+ 25\) min \(=\) 12:25 pm (see Diagrams).
Start: 2:40 pm. Finish: 3:25 pm. Count on: \(20\) min to 3:00 pm, then \(25\) min.
| \(20 + 25\) | \(=\) | \(45\) |
\(45\) minutes
(ii) In May 2026, Zoe’s cousin is \(12\) years \(7\) months old. In what month and year was he born?
(i) Count back: 8:15 am \(- 10\) min \(=\) 8:05 am; \(- 25\) min \(=\) 7:40 am; \(- 40\) min \(=\) 7:00 am.
(ii) May 2026 \(- 12\) years \(=\) May 2014; \(- 4\) months \(=\) January 2014; \(- 3\) months \(=\) October 2013.
| \(10 + 25 + 40\) | \(=\) | \(75\) |
(i) 7:00 am (check: \(75\) min \(= 1\) h \(15\) min after 7:00 am is 8:15 am)
(ii) October 2013
Time worked: \(40\) min to 9:00 am, \(4\) h to 1:00 pm, \(50\) min to 1:50 pm. That is \(4\) h \(90\) min \(= 5\) h \(30\) min \(= 5.5\) h.
| \(5 \times 19.20\) | \(=\) | \(96\) |
| \(0.5 \times 19.20\) | \(=\) | \(9.6\) |
| \(96 + 9.60\) | \(=\) | \(105.6\) |
Ruby earns \(\$105.60\).
(ii) A car park charges \(\$4.20\) for each hour or part of an hour. A car goes in at 10:20 am and comes out at 1:05 pm. How much does it cost?
| \(8 \times 16 + 7 \times 4\) | \(=\) | \(156\) |
| \(3 \times 4.20\) | \(=\) | \(12.60\) |
(i) \(8\) races have \(7\) gaps: \(156\) min \(= 2\) h \(36\) min, so the last race finishes at 11:36 am.
(ii) The car is parked \(2\) h \(45\) min, which is charged as \(3\) h: \(\$12.60\).
Change the landing time to town A time: 1:40 pm \(- 30\) min \(=\) 1:10 pm. Count on from 9:50 am: \(10\) min to 10:00 am, \(3\) h to 1:00 pm, \(10\) min to 1:10 pm.
| \(10 + 10\) | \(=\) | \(20\) |
The flight takes \(3\) h \(20\) min.
Common pitfalls
Frequently asked questions
How do you find a finish time?
Add the duration to the start time: hours first, then the minutes through the next o’clock.
How do you find the latest time to leave?
Start at the deadline and count back each step in order.
How do you work out pay for a shift?
Find the time worked, change it to decimal hours, then multiply by the hourly rate.
What does each hour or part of an hour mean?
Any started hour is charged as a whole hour: \(2\) h \(45\) min costs \(3\) hours.
How do you find when someone was born from their age?
Count back the years, then the months, from the date given.