Time and Elapsed Time Problems

Elapsed time is the amount of time that passes between a start time and an end time. To find it, count up from the start in friendly hops — full hours first, then the leftover minutes. The same idea works in reverse to find an end time when you know the start and the duration.

Reading the Clock

• On an analog clock the short hand shows the hour and the long hand shows the minutes.
• Each number on the clock face stands for 5 minutes, so the long hand on the 3 means 15 minutes past.
• Digital clocks show hours then minutes separated by a colon, like 9:15 or 11:45.
• AM means before noon (midnight to 12:00 noon); PM means after noon (12:00 noon to midnight).

Finding Elapsed Time — Count Up in Hops

1. Start at the start time. Hop full hours forward until you are still earlier than the end time.
2. Now hop minutes from there to the end time.
3. Add the hour hops and the minute hops together — that is the elapsed time.
4. Example: 9:15 AM to 11:45 AM. Hop 2 hours to 11:15. Hop 30 minutes to 11:45. Elapsed = 2 h 30 min.

Finding the End Time — Add the Duration

1. Add the hours of the duration to the start time first.
2. Then add the minutes. If the minutes go past 60, carry one extra hour.
3. Watch AM and PM — once you cross 12:00, the label flips.
4. Example: start 10:40 AM, duration 1 h 35 min. 10:40 + 1 h = 11:40. 11:40 + 35 min = 12:15 PM.

Tricky Boundaries

• Crossing noon: 11:30 AM + 2 h = 1:30 PM (the hour resets to 1 after 12).
• Crossing midnight: 10:50 PM + 2 h 20 min = 1:10 AM the next day.
• AM to PM problems: count to 12:00 first, then count the rest of the hours into PM.
• Always state the answer in hours and minutes (and AM or PM if asked).