Math Problem Statement

You start night shift at 22:00 and finish at 06:00 with a 45-minute break. How many hours do you work?

Solution

To calculate how many hours you work, we need to subtract the break from the total shift time.

  1. Start time: 22:00
  2. End time: 06:00 (the next day)
  3. Break: 45 minutes

First, calculate the total time between 22:00 and 06:00.

  • From 22:00 to midnight (00:00) = 2 hours
  • From 00:00 to 06:00 = 6 hours

So, the total shift time is:
2hours+6hours=8hours2 \, \text{hours} + 6 \, \text{hours} = 8 \, \text{hours}

Next, subtract the 45-minute break:

  • 45 minutes = 0.75 hours

Thus, the total working time is: 8hours0.75hours=7.25hours8 \, \text{hours} - 0.75 \, \text{hours} = 7.25 \, \text{hours}

You work 7.25 hours.

Would you like more details or have any questions?


Here are 5 related questions to further explore the concept:

  1. How would your working hours change if your break were 1 hour instead of 45 minutes?
  2. How many hours would you work over a 5-day workweek with this schedule?
  3. What is the total amount of break time in minutes across a 5-day week?
  4. How would the calculation differ if you worked a 10-hour shift with the same break?
  5. How would your total work hours change if you had two 30-minute breaks instead?

Tip: When calculating hours across midnight, split the time into two parts: from the start to midnight, and from midnight to the end.

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Math Problem Analysis

Mathematical Concepts

Time Calculation
Subtraction
Conversion between hours and minutes

Formulas

Total time = End time - Start time
Work hours = Total time - Break time
1 hour = 60 minutes

Theorems

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Suitable Grade Level

Grades 5-7