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Edexcel GCSE Maths (Higher) Study Notes

1.12.1 Calculating with Time

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

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

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.
3,600÷60=60 minutes3,600 \div 60 = 60 \text{ minutes}

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.
180÷60=3 hours180 \div 60 = 3 \text{ hours}

Calculating Time Differences

Determining the difference between two times is essential for planning and time management.

Unit of time

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:
15:4510:15=5 hours 30 minutes15:45 - 10:15 = 5 \text{ hours } 30 \text{ 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:
09:30+2:45=12:1509:30 + 2:45 = 12:15

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:
16:501:20=15:30 or 3:30 PM 16:50 - 1:20 = 15:30 \text{ or } 3:30 \text { PM }

Time Conversion Challenges

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

Time Zone conversion

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:

16:005=11:00 EST16:00 - 5 = 11:00 \text{ EST}

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