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Chapter 1: Problem 1

a. There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. Use these data to determine how many minutes are in a month. b. Now use the following data to calculate the number of minutes in a month: 24 hours per day, 60 minutes per hour, 7 days per week, and 4 weeks per month. c. Why are these answers different? Which (if any) is more correct? Why?

Short Answer

Expert verified
Using the first method (days and months per year), there are approximately 43,780 minutes in a month. Using the second method (weeks per month), there are 40,320 minutes in a month. The first method is more accurate because it takes into account the actual number of days in a year (365) and the actual number of months in a year (12) to calculate an average month length, while the second method simplifies a month to be composed of exactly 4 weeks, which is not always the case.

Step by step solution

01

Calculate Average Days per Month

\(AverageDaysPerMonth = \frac{365}{12} \approx 30.42\) #Step 2: Convert average days per month to hours# Now, we know that there are 24 hours per day, so to convert the average days in a month to hours, multiply the average days per month by 24: \[AverageHoursPerMonth = AverageDaysPerMonth \times 24\]
02

Calculate Average Hours per Month

\(AverageHoursPerMonth \approx 30.42 \times 24 \approx 729.67\) #Step 3: Convert average hours per month to minutes# Finally, there are 60 minutes per hour. To convert the average hours in a month to minutes, multiply the average hours per month by 60: \[AverageMinutesPerMonth = AverageHoursPerMonth \times 60\]
03

Calculate Average Minutes per Month

\(AverageMinutesPerMonth \approx 729.67 \times 60 \approx 43,780\) #b. Second method: Using weeks per month# #Step 1: Determine the number of days in a week-based month# Since there are 4 weeks per month, and each week is comprised of 7 days, multiply 4 by 7: \[WeekBasedDaysPerMonth = 4 \times 7\]
04

Calculate Week-Based Days per Month

\(WeekBasedDaysPerMonth = 4 \times 7 = 28\) #Step 2: Convert week-based days per month to hours# To convert week-based days per month to hours, multiply the week-based days per month (28) by the number of hours per day (24): \[WeekBasedHoursPerMonth = WeekBasedDaysPerMonth \times 24\]
05

Calculate Week-Based Hours per Month

\(WeekBasedHoursPerMonth = 28 \times 24 = 672\) #Step 3: Convert week-based hours per month to minutes# To convert week-based hours per month to minutes, multiply the week-based hours per month (672) by the number of minutes per hour (60): \[WeekBasedMinutesPerMonth = WeekBasedHoursPerMonth \times 60\]
06

Calculate Week-Based Minutes per Month

\(WeekBasedMinutesPerMonth = 672 \times 60 = 40,320\) #c. Compare the results and determine which is more correct#
07

Compare Results

The first method (using days per year and months per year) gives approximately 43,780 minutes per month, while the second method (using weeks per month) gives 40,320 minutes per month.
08

Determine More Correct Method

The first method is more accurate because it takes into account the actual number of days in a year (365) and the actual number of months in a year (12) to calculate an average month length. The second method simplifies a month to be composed of exactly 4 weeks, which is not always the case, as months can have 28, 29, 30, or 31 days, and some months can have both 4 or 5 weeks depending on the calendar. So, the first method provides a more precise measure of the number of minutes in a month because it considers the variations in the number of days per month.

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