Questions: Elapsed Time

Question 1

A movie starts at 2:45 PM and lasts 1 hour and 35 minutes. A student adds the times directly and gets 3:80 PM. What is wrong with this answer?

• A. The student forgot to add the hours portion correctly
• B. 3:80 is not a real time — minutes go up to 60, so the correct answer is 4:20 PM
• C. The student should have subtracted 1:35 instead of adding it
• D. The answer is almost right; 3:80 PM simply means 3 hours and 80 minutes

Answer: (B)

Time uses base-60: 60 minutes make one hour, not 100. When the raw addition gives 3:80, that 80 minutes must be converted — 80 minutes = 1 hour + 20 minutes. So 3 hours + 1 hour = 4 hours, with 20 minutes remaining: 4:20 PM. Option D is wrong because there is no such thing as 80 minutes on a clock. The base-60 trap is exactly why raw arithmetic on clock times fails.

Question 2

Why is the 'jump to the next whole hour first' strategy so effective for elapsed time problems?

• A. It avoids needing to know any multiplication
• B. It provides a clean anchor point that keeps you working with real clock positions, preventing base-60 errors
• C. It only works for problems where the elapsed time is less than one hour
• D. It only applies when working with AM times, not PM

Answer: (B)

Whole hours are anchor points where minutes reset to zero — clean, familiar positions on the clock. By jumping to the next whole hour first, you never have to do arithmetic that might push minutes past 60. Each jump stays within the rules of the base-60 system, so you can't accidentally produce '3:80' or similar nonsense. The strategy works for any elapsed time, including crossing noon (AM to PM).

Question 3

Using a jump strategy on a number line (e.g., jumping to the next whole hour, then adding remaining minutes) prevents the base-60 errors that happen with raw arithmetic.

• T. True
• F. False

Answer: True

Yes — the jump strategy keeps you anchored to real, valid clock times throughout the calculation. Each intermediate step is a real time you could see on a clock face. This sidesteps the base-60 problem entirely because you never do raw addition on clock digits. You work with the clock's actual structure rather than pretending minutes behave like base-10 digits.

Question 4

2:45 plus 1 hour and 35 minutes equals 3:80, because you simply add the hours (2+1=3) and the minutes (45+35=80) separately.

• T. True
• F. False

Answer: False

This is the classic base-60 error. When minutes add up to 60 or more, you must carry: 45 + 35 = 80 minutes = 1 hour and 20 minutes. Adding that extra hour to the 3 gives 4 hours total, so the correct answer is 4:20. '3:80' violates the base-60 system — there is no such time. You cannot treat clock arithmetic like ordinary base-10 addition.

Question 5

Why does calculating elapsed time require a different approach than ordinary addition? Describe what goes wrong when you treat clock times as base-10 numbers.

Model answer: Time uses base-60 for minutes (60 minutes = 1 hour), not base-10. If you treat clock digits like ordinary numbers and add 2:45 + 1:35, you get 3:80 — but 80 minutes doesn't exist on a clock. The minutes column 'overflows' at 60, not at 100. The fix is to use strategies that stay anchored to real clock positions, like jumping to the next whole hour first, so you never produce an invalid time.

The base-60 system is the core reason elapsed time requires special treatment. In base-10, every column overflows at 10; in time, the minutes column overflows at 60. Raw arithmetic ignores this and produces impossible times. Jump strategies work because they use the structure of the clock directly — you move from one real time to the next, always staying within valid clock positions, so the base-60 constraint is automatically satisfied.