POP

C1.15 Time

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01 — Explanation

How do I convert between the 12-hour and 24-hour clock?

12-hour	24-hour	Rule
$7{:}20$ am	`07 20`	Morning: keep the hour, add a leading zero if needed
$12{:}00$ noon	`12 00`	Stays as $12$
$4{:}05$ pm	`16 05`	Afternoon/evening: add $12$ to the hour
$12{:}30$ am	`00 30`	Just after midnight: subtract $12$

Common Slip

writing a 24-hour time with "am" or "pm" attached, e.g. 15:45 pm. The 24-hour clock never uses am/pm — the hour value alone tells you the time of day.

02 — Explanation

How do I add or subtract time, especially across midnight?

Time runs in base 60, not base 10 — you can't just add decimals. Work in hours and minutes separately, and carry over whenever minutes reach $60$ or the hour reaches $24$ .

Example: a train departs at 23 10 and the journey takes $3$ hours $55$ minutes. Find the arrival time.

Add the hours: $23{:}10 + 3\text{ h} = 26{:}10$ .
Since this is $\geqslant 24{:}00$ , subtract $24$ hours to move into the next day: $26{:}10 - 24{:}00 = 02{:}10$ (next day).
Add the remaining $55$ minutes: $02{:}10 + 55\text{ min} = 03{:}05$ .
Final answer: 03 05, the following day.

03 — Explanation

How do I convert between minutes and decimal hours?

Divide minutes by $60$ to get a decimal fraction of an hour.

Example: write $2$ hours $21$ minutes as a decimal number of hours.

$21 \div 60 = 0.35$ hours.
Add to the whole hours: $2 + 0.35 = 2.35$ hours.

Common Slip

writing $2$ hours $21$ minutes as $2.21$ hours directly — the minutes must go through the $\div 60$ step first.

04 — Explanation

How do I solve problems involving time zones or local time differences?

Time zones are usually given as an offset from a reference time (such as "3 hours ahead" or "5 hours behind"). To find the local time somewhere else, add the offset if that place is ahead, or subtract it if it's behind — then apply the same carrying rules as any other time calculation.

Example: it is 09 00 in London. Dubai is $4$ hours ahead of London, and Los Angeles is $8$ hours behind London. A flight leaves London at 09 00 and takes $7$ hours to reach Dubai. What is the local time in Dubai when the flight lands, and what is the local time in Los Angeles at that same moment?

Landing time in London time: $09{:}00 + 7\text{ h} = 16{:}00$ .
Convert to Dubai local time (4 hours ahead): $16{:}00+4\text{ h}=20{:}00$ .
Convert the same instant to Los Angeles local time (8 hours behind London): $16{:}00-8\text{ h}=08{:}00$ .

Exam Tip

always do the "how much time has passed" calculation in one consistent time zone first (usually the departure city's), and only convert to the destination's local time as the very last step — mixing zones partway through a calculation is a common source of errors.

05 — Common mistakes

Common mistakes to avoid

Writing minutes as the decimal part directly, without dividing by $60$ first.
Forgetting to carry over when a total reaches $60$ minutes or $24$ hours, e.g. leaving a total as 02:75 instead of converting to 03:15.
Adding "am"/"pm" to a 24-hour time.