Calculating Arnold's Work Hours Using Proportion and Unit Rate

Arnold works 60 hours every three weeks. This article will explore how to calculate the total number of hours he works in 12 weeks using both the unit rate method and the proportion method. We'll break down the steps and provide a clear explanation to ensure a thorough understanding of the problem.

Understanding Arnold's Work Schedule

Arnold works 60 hours every three weeks. To simplify this, we can determine the number of hours he works per week using the unit rate method. The unit rate is the amount of work per basic unit of time. Here, that unit of time is one week.

Unit Rate Method

To find the unit rate, we divide the total hours by the number of weeks:

Unit rate 60 hours / 3 weeks

Unit rate 20 hours/week

Calculating the Total Hours for 12 Weeks

Now that we know Arnold works 20 hours per week, we can easily calculate the total number of hours he will work in 12 weeks by multiplying the weekly unit rate by the number of weeks:

Total hours 20 hours/week * 12 weeks

Total hours 240 hours

Proportion Method

We can also solve this problem using the proportion method. This method involves setting up a ratio and then solving for the unknown quantity. Here's how:

60 hours : 3 weeks t hours : 12 weeks

Using cross multiplication:

3t 12 * 60

3t 720

t 720 / 3

t 240 hours

Another Approach Using Multiplication

An alternative method involves recognizing that 12 weeks is 4 times 3 weeks:

12 weeks 3 weeks * 4

Therefore, Arnold's total hours for 12 weeks can be calculated as:

t 60 hours * 4

t 240 hours

Conclusion

In summary, whether we use the unit rate method, the proportion method, or multiplication, we can determine that Arnold works 240 hours in 12 weeks. This straightforward calculation can be applied to similar problems, helping you quickly gauge work hours based on a given weekly or monthly schedule.

Frequently Asked Questions

How can I verify the calculation?

Simply double-check the multiplication and division steps. In the unit rate method, ensure that 60 divided by 3 equals 20, and then multiply 20 by 12. In the proportion method, confirm that 3t equals 720, and then solve for t. With the multiplication approach, verify that 60 multiplied by 4 equals 240.

What if the problem changes to a different number of weeks?

The same methods apply. Adjust the number of weeks in both the unit rate method and the proportion method accordingly. For example, if the problem was for 18 weeks, you would calculate 20 hours/week * 18 weeks for the unit rate method or set up the proportion as 60 hours : 3 weeks t hours : 18 weeks.

Can this be applied to other work schedules?

Yes, this method is versatile and can be used to calculate hours for any consistent work schedule, provided the weekly number of hours is known. Whether it's for salaried employees or hourly workers, this approach will help in determining the total hours worked over a specified period.