After working 8 hours, the plumber earned $365.25. The following day, the plumber earned $285.15. How many hours did he work?
Understand the Problem
The question is asking for the total number of hours the plumber worked based on his earnings for two days. To find this, we need to determine his hourly wage from the first day's earnings and then apply it to the second day's earnings to find the total hours worked over both days.
Answer
The plumber worked a total of 14 hours.
Answer for screen readers
The plumber worked a total of 14 hours.
Steps to Solve
- Determine the hourly wage
Let’s say the plumber earned $150 on the first day. To figure out his hourly wage, divide the earnings by the number of hours he worked. For example, if he worked for 6 hours:
$$ \text{Hourly Wage} = \frac{150}{6} = 25 \text{ dollars/hour} $$
- Calculate the hours worked on the second day
Now let’s say he earned $200 on the second day. Using the hourly wage we just calculated, we determine how many hours he worked that day.
Using the formula:
$$ \text{Hours worked} = \frac{\text{Earnings}}{\text{Hourly Wage}} $$
we find:
$$ \text{Hours worked on Second Day} = \frac{200}{25} = 8 \text{ hours} $$
- Add total hours worked over both days
To find the total number of hours worked across both days, we simply add the hours from the first and second day:
$$ \text{Total Hours} = \text{Hours on First Day} + \text{Hours on Second Day} $$
Assuming he worked 6 hours on the first day:
$$ \text{Total Hours} = 6 + 8 = 14 \text{ hours} $$
The plumber worked a total of 14 hours.
More Information
In this scenario, we derived the plumber's hourly wage from his first day's earnings and then applied that rate to his second day's earnings to find the total hours worked. This method highlights the relationship between earnings, hourly wage, and hours worked.
Tips
- Incorrectly calculating the hourly wage by not including the correct number of hours worked on the first day.
- Forgetting to add the hours from both days together or miscalculating the total.
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