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.

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• 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.

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.

Example 3: Time Difference in Hours and Minutes

Question: Find the time difference between 10:15 AM and 3:45 PM.

Solution:

1. Convert to 24-hour time: 10:15 stays the same, 3:45 PM becomes 15:45.
2. 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:

1. 9:30 AM in 24-hour format is 09:30.
2. Add hours and minutes:

Example 5: Subtracting Time

Question: What time is it 1 hour and 20 minutes before 4:50 PM?

Solution:

1. Convert 4:50 PM to 24-hour format: 16:50.
2. Subtract the time duration:

Time Conversion Challenges

Applying these concepts to solve real-world problems, like time zone conversions, enhances understanding and practical skills.

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: