Use units of time, convert between 12-hour and 24-hour time, and solve problems involving elapsed time and the addition and subtraction of time

Award one mark for handling the noon crossing correctly: from $11{:}40$ am to $12{:}00$ noon is $20$ min, plus $12{:}00$ to $12{:}25$ pm is $25$ min, giving a scheduled journey time of $45$ min (1 mark). For part (b), the actual departure is $11{:}48$ am, so the actual journey is $12{:}25 - 11{:}48 = 37$ min (1 mark), and the reduction is $45 - 37 = 8$ min (1 mark). A marker rewards the explicit split at noon; a candidate who writes $12{:}25 - 11{:}40$ and treats it as $0$ h $85$ min or $1$ h $15$ min loses the accuracy marks. Note the journey-time reduction equals the lateness, which is a sensible check.

Part (a): $10{:}30$ pm $= 22{:}30$ and $6{:}15$ am $= 06{:}15$ (1 mark for both). Part (b): split at midnight - $22{:}30$ to midnight is $1$ h $30$ min and midnight to $06{:}15$ is $6$ h $15$ min, total $7$ h $45$ min (1 mark; a marker accepts a clean 24-hour subtraction treating $06{:}15$ as $30{:}15$). Part (c): convert $7$ h $45$ min to $7.75$ hours, then $7.75 imes 28.40 = 220.10$, so $220.10 (1 mark for $7.75$ h, 1 mark for the final amount). The classic error is using $7.45$ hours instead of $7.75$; markers penalise it because $45$ minutes is $frac{45}{60} = 0.75$ of an hour, not $0.45$.

Part (a): $2{:}50$ pm $= 14{:}50$ (1 mark). Part (b): add the duration to $14{:}50$ - adding $2$ h gives $16{:}50$, then adding $50$ min gives $17{:}40$, which is $5{:}40$ pm (1 mark for $17{:}40$, 1 mark for the matching $5{:}40$ pm). A marker looks for the carry handled correctly when the minutes pass $60$: $50 + 50 = 100$ min $= 1$ h $40$ min, so the hour rolls from $16$ to $17$. A candidate who writes $16{:}100$ or forgets to carry loses the finish-time mark.

Part (a) - hours are bigger than minutes, so multiply, then add. One hour is $60$ minutes, so

and adding the extra $35$ minutes gives $120 + 35 = 155$ minutes.

Part (b) - seconds are smaller than minutes and hours, so divide. First turn seconds into minutes by dividing by $60$:

Then turn minutes into hours by dividing by $60$ again:

So $9000$ s $= 2$ h $30$ min $0$ s. (Check: $2 \times 3600 + 30 \times 60 = 7200 + 1800 = 9000$ s.)

Part (a) - it is pm and not $12$, so add $12$ to the hours. Afternoon and evening times past $12{:}59$ pm are written by adding $12$ to the hour:

so $2{:}45$ pm $= 14{:}45$.

Part (b) - it is am, so the 24-hour hours match (with a leading zero). Morning times keep the same hour but are padded to two digits:

(Reminder: $12$ am is midnight $= 00{:}00$, and $12$ pm is noon $= 12{:}00$ - these two are the cases people get wrong.)

Count up to the next whole hour

From $8{:}15$ am to $9{:}00$ am is $45$ minutes.

Count the whole hours

From $9{:}00$ am to $11{:}00$ am is $2$ hours.

Count the last part

From $11{:}00$ am to $11{:}50$ am is $50$ minutes.

Add the parts

The minutes give $45 + 50 = 95$ minutes $= 1$ hour $35$ minutes, so the total is

The trip takes $3$ hours $35$ minutes. (Both times are am, so there is no noon crossing to worry about here.)

Part (a) - add the hours first, then the minutes. Start at $7{:}45$ pm and add $2$ hours:

Now add the $40$ minutes. From $9{:}45$ pm, the first $15$ minutes reach $10{:}00$ pm, leaving $40 - 15 = 25$ minutes:

The film finishes at $10{:}25$ pm.

Part (b) - convert both to 24-hour time. Both are pm and not $12$, so add $12$ to each hour:

So the session runs from $19{:}45$ to $22{:}25$. (Check: $22{:}25 - 19{:}45 = 2$ h $40$ min, the stated running time.)

Split the journey at noon (the am/pm change). This is the safe way to cross $12{:}00$ - never subtract the raw clock numbers across noon.

First part: up to noon. From $10{:}25$ am to $12{:}00$ noon:

Second part: after noon. From $12{:}00$ noon to $1{:}10$ pm is

Add the two parts.

The travel time is $2$ hours $45$ minutes. (Cross-check in 24-hour time: $13{:}10 - 10{:}25 = 2$ h $45$ min, which agrees.)

Part (a) - the shift crosses midnight, so split it there. Work out the time to midnight, then the time after midnight, then add.

Up to midnight. From $10{:}30$ pm to $12{:}00$ midnight:

After midnight. From $12{:}00$ midnight to $6{:}45$ am is

Add the two parts.

so the nurse is at work for $8$ hours $15$ minutes.

Part (b) - subtract the unpaid break. Take the $30$-minute meal break off the time at work:

So $7$ hours $45$ minutes are paid. (Working in 24-hour time gives the same span: $6{:}45$ am is $06{:}45$, which is $30{:}45$ on the next day's running clock, and $30{:}45 - 22{:}30 = 8$ h $15$ min.)

Part (a) - add the duration, crossing midnight. Add the hours first: $11{:}50$ pm $+ 6$ h $= 5{:}50$ am (Wednesday, since we passed midnight). Now add the $35$ minutes:

So the flight arrives at $6{:}25$ am on Wednesday.

Part (b) - convert to 24-hour time. Departure $11{:}50$ pm is pm and not $12$, so add $12$: $11 + 12 = 23$, giving $23{:}50$. Arrival $6{:}25$ am is a morning time, padded to $06{:}25$. So the flight runs $23{:}50$ Tuesday to $06{:}25$ Wednesday. (Check: from $23{:}50$ to $24{:}00$ is $10$ min, and $10$ min $+ 6$ h $25$ min $= 6$ h $35$ min, the stated flight time.)

Part (c) - find when the sleep ends. Sleep starts $1$ h $15$ min after departure. Departure is $23{:}50$, so add $1$ h $15$ min:

Then add the $4$ hours of sleep:

So the sleep period ends at $05{:}05$. (This is $1$ h $20$ min before the $06{:}25$ landing, a sensible buffer.)