In this section, we delve into the fundamentals of calculating with time, focusing on understanding and converting between different time units and mastering the 24-hour and 12-hour clock systems. These skills are pivotal for navigating daily tasks, academic challenges, and understanding complex time-related concepts.
Understanding Time Units
Time is segmented into various units, but for our purposes, we concentrate on seconds, minutes, and hours:
- Seconds (s): The smallest commonly used unit of time. There are 60 seconds in a minute.
- Minutes (min): A medium-sized unit of time. There are 60 minutes in an hour.
- Hours (h): Used for longer durations of time. A day is divided into 24 hours.
The 24-hour Clock System
The 24-hour clock system spans from 0:00 to 23:59, offering a precise method for representing the time of day without the need for AM and PM distinctions.
![24-hour clock](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F64ea1b6e-9f3f-41c8-8db9-10bb26a82399-file.png&w=828&q=75)
Image courtesy of Practical Pages
- Conversion to 24-hour format: PM times are converted by adding 12 to the hour portion.
- Conversion to 12-hour format: For hours greater than 12, subtract 12 to find the PM time.
![24-hour and 12-hour conversion](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F32d00538-a2a3-4e91-8754-ea7dc6b77d4a-file.png&w=1200&q=75)
Image courtesy of 24-hour watch
Calculating with Different Time Units
Efficient calculation with time necessitates fluency in converting between seconds, minutes, and hours.
Example 1: Converting Seconds to Minutes
Question: Convert 3,600 seconds into minutes.
Solution:
- We know 1 minute = 60 seconds.
- Therefore, to convert seconds to minutes, we divide by 60.
Example 2: Converting Minutes to Hours
Question: How many hours are in 180 minutes?
Solution:
- 1 hour = 60 minutes.
- To find hours, divide the minutes by 60.
Calculating Time Differences
Determining the difference between two times is essential for planning and time management.
![Unit of time](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F3e951301-882d-4d58-9ee3-f382ef8009a5-file.png&w=828&q=75)
Example 3: Time Difference in Hours and Minutes
Question: Find the time difference between 10:15 AM and 3:45 PM.
Solution:
- Convert to 24-hour time: 10:15 stays the same, 3:45 PM becomes 15:45.
- Subtract the start time from the end time, taking care to align hours and minutes:
Adding and Subtracting Time
Operations with time must consider the base 60 nature of minutes and hours.
Example 4: Adding Time
Question: What is the time 2 hours and 45 minutes after 9:30 AM?
Solution:
- 9:30 AM in 24-hour format is 09:30.
- Add hours and minutes:
Example 5: Subtracting Time
Question: What time is it 1 hour and 20 minutes before 4:50 PM?
Solution:
- Convert 4:50 PM to 24-hour format: 16:50.
- Subtract the time duration:
Time Conversion Challenges
Applying these concepts to solve real-world problems, like time zone conversions, enhances understanding and practical skills.
![Time Zone conversion](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fd20a5ba1-f77c-46ea-8a6d-8cc0396bbf1b-file.png&w=1920&q=75)
Question: If it is 4:00 PM in London (GMT), what time is it in New York (EST), given EST is 5 hours behind GMT?
Solution: