Chanukah Math

We learned the following rules related to lighting the menorah:

• Ideally, candles should be lit at tzeit ha-kochavim (when three stars appear)
• Candles must burn for 30 minutes from the time they are lit.
• On Shabbat, we light the menorah slightly earlier, before sundown, to circumvent the prohibition of hav'arah (kindling a flame).

Based on these rules, students responded to scenarios like the following:

If tzeit ha-kochavim is at 6:00 PM, until what time would the candles have to burn? (6:30 PM)

If the candles burned until 6:45 PM, what time must you have lit the menorah? (6:15 PM)

It's erev shabbat. If sundown is at 5:45 PM and tzeit ha-kochavim is at 6:20 PM, until what time must the candles burn? (6:50 PM, for 1 hour 5 minutes).