Determine the time difference between two places given their time zones or UTC offsets, and solve problems involving the International Date Line and the local time of arrival after a journey, allowing for the change of date when crossing the line

Award one mark for the correct time difference, $(+10) - 0 = 10$ hours, with Sydney ahead. Award one mark for adding (not subtracting) $10$ hours because Sydney is ahead of London: $16{:}00 + 10{:}00 = 26{:}00$. Award the final mark for converting the rollover correctly, $26{:}00 - 24{:}00 = 02{:}00$ the next day, and stating Wednesday $2{:}00$ am. A common error is subtracting the $10$ hours (treating Sydney as behind), which loses the second and third marks; another is keeping $26{:}00$ without rolling over the day.

Award one mark for the zone change $(-7) - (+10) = -17$ hours. Award one mark for combining departure, flight and zone change: $09{:}00 + 14{:}00 = 23{:}00$, then $23{:}00 - 17{:}00 = 06{:}00$. Award one mark for the day: the total stays within the same day, so arrival is $6{:}00$ am on Wednesday, the same calendar day as departure. Award the final mark for the explanation that travelling east across the date line subtracts a day, which offsets the day the flight would otherwise have added, so the local clock can read earlier than departure. Markers penalise students who add $17$ hours instead of subtracting, or who fail to mention the date-line direction.

Award one mark for the eastbound ship: crossing the line travelling east subtracts a day, so its date becomes Friday (the date is repeated). Award one mark for the westbound ship: crossing travelling west adds a day, so its date becomes Sunday (a date is skipped). Award the final mark for the justification that the date line is where each new calendar day begins, so the two directions of crossing change the date in opposite ways, even though both ships experience the same instant of time. The frequent error is mixing up the directions; anchoring on west-adds, east-subtracts secures the marks.

Subtract the two offsets. The time difference is the gap between the offsets:

State which is ahead. Sydney has the larger (more positive) offset, so Sydney is ahead. The two cities are $17$ hours apart, with Sydney $17$ hours ahead of Los Angeles. (A useful check: a place further east has a larger offset and runs ahead, and Sydney is east of Los Angeles.)

Find the difference. Subtract the offsets:

and Perth (the larger offset) is ahead.

Apply it the right way. New York is behind Perth, so subtract $13$ hours from $3$ pm. In $24$-hour time $3$ pm is $15{:}00$:

so it is $2$ am in New York. (Going to a place that is behind you, the clock reads earlier, so you subtract.)

Part (a) - subtract the offsets. Both offsets are positive:

so the cities are $5$ hours $30$ minutes apart, with Adelaide ahead.

Part (b) - apply the difference. Dubai is behind Adelaide, so subtract $5$ hours $30$ minutes. In $24$-hour time $7{:}00$ pm is $19{:}00$:

so it is $1{:}30$ pm in Dubai. (The half-hour offset is the trap here: Adelaide is one of the zones that is not a whole number of hours from UTC.)

Note the zone change is zero. Both cities are at UTC $+8$, so there is no time-zone adjustment: only the flight duration changes the clock.

Add the flight duration to the departure time. Departure is $07{:}00$. Add $5$ hours to reach $12{:}00$, then add the $20$ minutes:

so the plane lands at $12{:}20$ pm Singapore time, on the same day. (Because the offsets match, this is just an elapsed-time question; the time-zone work only matters when the offsets differ.)

Find the zone change. Tokyo minus Sydney is

so Tokyo is $1$ hour behind Sydney; the clock goes back $1$ hour on arrival.

Add the flight duration, then apply the zone change. Start at $09{:}15$ and add the flight time:

then take off the $1$ hour zone change:

so the plane lands at $18{:}00$, that is $6{:}00$ pm, Tokyo time on the same day. (No date line is crossed, so the date does not jump; only the flight time and the small zone change move the clock.)

Find the zone change. Sydney minus Los Angeles is

so Sydney is $17$ hours ahead. Travelling from Los Angeles to Sydney the clock jumps forward $17$ hours.

Add the flight time and the zone change to the departure time. Start at Friday $10{:}30$, add the $14$ hours $30$ minutes of flight and the $+17$ hours of zone change:

Convert the total back to a clock time and count the days. Every $24$ hours is one whole day, so subtract $24$:

which is one day rolled over. The plane leaves Friday and lands at $18{:}00$ (that is $6{:}00$ pm) on Saturday. Going west across the International Date Line, the date moves forward, so although the flight is under a day the calendar shows the next day.

Part (a) - zone change. Los Angeles minus Sydney is

so Los Angeles is $17$ hours behind Sydney; the clock jumps back $17$ hours.

Part (b) - arrival time and day. Start at Monday $11{:}30$, add the flight time, then apply the $-17$ hour zone change:

The total stays inside the same day, so the plane lands at $8{:}00$ am on Monday (Los Angeles time). Travelling east across the International Date Line subtracts a day, which is exactly what cancels the day that the long flight added.

Part (c) - why it looks earlier. The flight lasts $13$ hours $30$ minutes, but Los Angeles is $17$ hours behind Sydney. Because the time you "win back" from the time zones ($17$ hours) is larger than the time spent flying ($13.5$ hours), the local clock at the destination reads $3.5$ hours earlier than departure, so you appear to land before you took off. No time is actually lost: only the local clocks differ.