Problem
Daylight length from sunrise and sunset
A table gives sunrise and sunset for three days. Daylight runs from sunrise to sunset, and night is 24 hours minus daylight. Find the day with the longest daylight and the length of its night.
Reasoning · Grade 2-2 Time and Duration
Your answer
Watch out Finding the longest daylight feels like finishing, but the question wants 24 hours minus that daylight.
How to solve
Strategy Identify Subproblems — Break the task into small pieces: first compute each day's daylight (sunset minus sunrise), then pick the longest, then get night by subtracting that daylight from 24 hours. Each piece is a simple elapsed-time calculation.
1STEP 1
Find the daylight on January 3
Splitting Jan 3 at noon gives 9 h 40 min.
12 h - 2 h 20 min = 9 h 40 min
Splitting the span at noon turns a tricky a.m.-to-p.m. gap into two easy elapsed-time pieces.
3.MD.A.1Identify Subproblems2STEP 2
Find the daylight on January 7
The same split makes Jan 7 9 h 50 min.
4 h 25 min + 5 h 25 min = 9 h 50 min
Same split-at-noon idea keeps the minutes easy to add.
3.MD.A.1Identify Subproblems3STEP 3
Find the daylight on January 12
Jan 12 comes out at exactly 10 hours.
4 h 30 min + 5 h 30 min = 10 h 0 min
Adding two halves that each end in 30 minutes makes a whole extra hour, giving a clean 10 hours.
3.MD.A.1Identify Subproblems4STEP 4
Pick the longest daylight
Comparing the three, the longest daylight is Jan 12.
Both sunrise moving earlier and sunset moving later add daylight, so the latest day in the table has the most daylight.
3.MD.A.1Look For A Pattern5STEP 5
Find the night on that day
That night is 24 − 10 = 14 hours.
24 h - 10 h = 14 h
Day and night together must fill the 24-hour day, so subtracting daylight from 24 gives the night.
3.MD.A.1Identify SubproblemsThe night is what is left of the 24-hour day once the daylight is taken away.
Why?
Daylight and night fill the whole day between them with no gap and no overlap, so together they are exactly 24 hours.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Knowing the whole day and the daylight part, subtracting returns the other part, because taking away undoes putting together.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Answer
14 hours
24 − 10 = 14
In early January the days are short, so a daylight of about 10 hours and a night of about 14 hours is sensible (more night than day in winter). Daylight 10 h + night 14 h = 24 h, which is exactly one full day, so the answer checks out.
Takeaway
Split each sunrise-to-sunset span at noon to find daylight, then subtract from 24 hours for the night. Pure Grade 3 elapsed-time thinking!
- Find the daylight on January 3
- Find the daylight on January 7
- Find the daylight on January 12
- Pick the longest daylight
- Find the night on that day