Mathematics
Grade 9
15 min
Elapsed time
Elapsed time
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1
Introduction & Learning Objectives
Learning Objectives
Calculate the duration between a start and end time, including scenarios that cross AM/PM and midnight.
Determine the end time given a start time and a duration, and vice versa.
Convert fluently between 12-hour (AM/PM) and 24-hour (military) time formats to simplify calculations.
Solve multi-step word problems involving elapsed time, including those that span multiple time zones.
Apply algebraic methods to model and solve problems where time is a variable.
Interpret and calculate time intervals from functional relationships or graphs.
A flight from Tokyo to New York crosses 13 time zones and the International Date Line. How do you calculate the actual flight time? ✈️ Let's unravel the mathematics of time.
This tutorial moves beyond simple clock arit...
2
Key Concepts & Vocabulary
TermDefinitionExample
Elapsed Time (Duration)The amount of time that passes from the beginning of an event (start time) to its end (end time). It is a measure of duration, not a specific point in time.If a movie starts at 7:10 PM and ends at 9:25 PM, the elapsed time is 2 hours and 15 minutes.
12-Hour Clock (AM/PM)A time convention in which the 24 hours of the day are divided into two periods: a.m. (ante meridiem, 'before midday') and p.m. (post meridiem, 'after midday').3:00 PM is in the afternoon, while 3:00 AM is in the early morning.
24-Hour Clock (Military Time)A time convention in which the day runs from midnight to midnight and is divided into 24 hours, numbered from 00 to 23. It eliminates the need for AM/PM.3:00 PM is represented as 15:00. 12:30 AM is represen...
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Core Formulas
Elapsed Time Calculation
T_{elapsed} = T_{end} - T_{start}
To find the duration, subtract the start time from the end time. It's often easiest to convert to 24-hour format first. If the end time's minutes are less than the start time's minutes, you must 'borrow' 60 minutes from the hour.
Finding an End Time
T_{end} = T_{start} + T_{elapsed}
To find the end time, add the duration to the start time. If the minutes add up to 60 or more, carry over the appropriate number of hours. Be mindful of crossing midnight (24:00).
Time Zone Conversion
T_{new} = T_{original} + (\text{Offset}_{new} - \text{Offset}_{original})
To convert a time from one time zone to another, find the difference in their UTC offsets and add it to the original time. For example...
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Challenging
A scientific experiment begins at 8:00 AM. The temperature T, in degrees Celsius, of a substance after 'm' minutes is modeled by T(m) = 0.05m² + m + 15. The first phase of the experiment ends when the temperature reaches 35°C. The second phase begins immediately and lasts for a duration equal to one-third of the first phase's duration. At approximately what time does the second phase end?
A.8:16 AM
B.8:18 AM
C.8:21 AM
D.8:25 AM
Challenging
A traveler flies from Sydney (UTC+10) to Dubai (UTC+4) on a 14-hour flight. After a 4-hour layover, they fly from Dubai to Rio de Janeiro (UTC-3) on a 15-hour flight. If they depart Sydney at 06:00 on Monday, what is the local time and day of their final arrival in Rio?
A.16:00 on Tuesday
B.23:00 on Monday
C.09:00 on Tuesday
D.19:00 on Monday
Challenging
The height h (in meters) of a model rocket 't' seconds after launch is modeled by the function h(t) = -5t² + 60t. For safety, a parachute must be deployed while the rocket is at or above a height of 160 meters. For how long is the rocket within the safe deployment zone?
A.10 seconds
B.4 seconds
C.8 seconds
D.6 seconds
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