A table needs to be completed with time zone calculations for Rio de Janeiro and Berlin, given UTC time and their longitudes.

here is the completed table for Question 4:

To complete the table, we use the following relationships:

• The Earth rotates $360^\circ$ in 24 hours.
• This means 1 hour corresponds to $15^\circ$ of longitude ($360^\circ / 24 \text{ hours} = 15^\circ/\text{hour}$).
• Conversely, $1^\circ$ of longitude corresponds to 4 minutes ($60 \text{ minutes} / 15^\circ = 4 \text{ minutes}/^\circ$).
• Locations East of UTC are ahead in time, and locations West of UTC are behind in time.
• UTC time is given as 12:00.

Here are the calculations for each row:

Rio de Janeiro:

• Longitude of Rio de Janeiro is approximately $43^\circ\text{W}$.
• Difference in degrees: $43^\circ$.
• Difference in time: $43^\circ \times \frac{1 \text{ hour}}{15^\circ} = 2.866... \text{ hours} = 2 \text{ hours and } (0.866 \times 60) \text{ minutes} = 2 \text{ hours } 52 \text{ minutes}$.
• Ahead/Behind: West of UTC, so Behind.
• Time: $12:00 - 2 \text{ hours } 52 \text{ minutes} = 09:08$.

Berlin:

• Longitude of Berlin is approximately $13^\circ\text{E}$.
• Difference in degrees: $13^\circ$.
• Difference in time: $13^\circ \times \frac{1 \text{ hour}}{15^\circ} = 0.866... \text{ hours} = 0 \text{ hours and } (0.866 \times 60) \text{ minutes} = 0 \text{ hours } 52 \text{ minutes}$.
• Ahead/Behind: East of UTC, so Ahead.
• Time: $12:00 + 0 \text{ hours } 52 \text{ minutes} = 12:52$.

Perth:

• Longitude of Perth is approximately $116^\circ\text{E}$.
• Difference in degrees: $116^\circ$.
• Difference in time: $116^\circ \times \frac{1 \text{ hour}}{15^\circ} = 7.733... \text{ hours} = 7 \text{ hours and } (0.733 \times 60) \text{ minutes} = 7 \text{ hours } 44 \text{ minutes}$.
• Ahead/Behind: East of UTC, so Ahead.
• Time: $12:00 + 7 \text{ hours } 44 \text{ minutes} = 19:44$.

Tehran (first entry):

• Given: Difference in time is $3.5 \text{ hours}$.
• Difference in degrees: $3.5 \text{ hours} \times 15^\circ/\text{hour} = 52.5^\circ$.
• Ahead/Behind: Since the time is later than UTC (as indicated by the $3.5 \text{ hours}$ ahead), it is Ahead.
• Time: $12:00 + 3 \text{ hours } 30 \text{ minutes} = 15:30$.

Tehran (second entry):

• Given: Ahead, Time is $15:30$.
• Difference in time: $15:30 - 12:00 = 3 \text{ hours } 30 \text{ minutes} = 3.5 \text{ hours}$.
• Difference in degrees: $3.5 \text{ hours} \times 15^\circ/\text{hour} = 52.5^\circ$.
• Ahead/Behind: Ahead (pre-filled).

Here is the completed table:

COUNTRY	DIFFERENCE IN $\text{IN }^\circ$	DIFFERENCE IN TIME	AHEAD/BEHIND OF THE UTC	TIME
Rio de Janeiro	$\boxed{\text{43}^\circ}$	$\boxed{\text{2.87 hrs (2h 52m)}}$	$\boxed{\text{Behind}}$	$\boxed{\text{09:08}}$
Berlin	$\boxed{\text{13}^\circ}$	$\boxed{\text{0.87 hrs (0h 52m)}}$	$\boxed{\text{Ahead}}$	$\boxed{\text{12:52}}$
Perth	$\boxed{\text{116}^\circ}$	$\boxed{\text{7.73 hrs (7h 44m)}}$	$\boxed{\text{Ahead}}$	$\boxed{\text{19:44}}$
Tehran	$\boxed{\text{52.5}^\circ}$	$\boxed{\text{3.5 hrs}}$	$\boxed{\text{Ahead}}$	$\boxed{\text{15:30}}$
Tehran	$\boxed{\text{52.5}^\circ}$	$\boxed{\text{3.5 hrs}}$	Ahead	15:30