Find start and end times

Learning Objectives Calculate an end time given a start time and a duration, crossing AM/PM and midnight boundaries. Calculate a start time by working backward from a known end time and duration. Convert fluently between 12-hour (AM/PM) and 24-hour (military) time formats to simplify calculations. Solve multi-step word problems involving multiple durations, such as work periods and breaks. Incorporate time zone conversions (e.g., UTC offsets) to find start or end times for international events. Determine start or end times in problems involving rates, such as speed, distance, and time. Planning a video call with a friend in another country? 🌍 Let's master the math to ensure no one shows up three hours early or late! This tutorial moves beyond basic time calculations....

TermDefinitionExample Duration (Elapsed Time)The amount of time that passes between a start time and an end time.The duration between 8:30 AM and 11:10 AM is 2 hours and 40 minutes. 24-Hour Time (Military Time)A timekeeping convention where the day runs from midnight to midnight and is divided into 24 hours, numbered from 0 to 23. It eliminates the need for AM/PM.3:45 PM is represented as 15:45 in 24-hour time. Time ZoneA region of the globe that observes a uniform standard time for legal, commercial, and social purposes.New York is in the Eastern Time Zone (ET), which is typically UTC-5 (or UTC-4 during daylight saving). UTC (Coordinated Universal Time)The primary time standard by which the world regulates clocks and time. It is the reference point for all other time zones, which are exp...

Finding the End Time T_{end} = T_{start} + \Delta t To find the end time (T_end), add the duration (delta t) to the start time (T_start). It is often easiest to convert all times to a common unit (like minutes) or use 24-hour format to avoid AM/PM errors. Finding the Start Time T_{start} = T_{end} - \Delta t To find the start time (T_start), subtract the duration (delta t) from the end time (T_end). 'Borrowing' an hour (60 minutes) is often necessary during subtraction. Time Zone Conversion T_{local} = T_{UTC} + \text{Offset} To find the local time in a specific time zone, add the time zone's offset to the Coordinated Universal Time (UTC). The offset can be positive (ahead of UTC) or negative (behind UTC).