Nathan packs 25 boxes in 2 hours. How many boxes can he pack in an 8-hour shift?
Understand the Problem
The question is asking how many boxes Nathan can pack in an 8-hour shift, given that he packs 25 boxes in 2 hours. We can solve this by first determining his rate of packing boxes per hour and then multiplying that by 8 hours.
Answer
100 boxes
Answer for screen readers
Nathan can pack 100 boxes in an 8-hour shift.
Steps to Solve
- Determine Nathan's packing rate
First, find out how many boxes Nathan can pack in one hour. He packs 25 boxes in 2 hours, so we calculate his rate as follows:
$$ \text{Rate} = \frac{\text{Total boxes}}{\text{Total hours}} = \frac{25 \text{ boxes}}{2 \text{ hours}} = 12.5 \text{ boxes per hour} $$
- Calculate total boxes packed in 8 hours
Now that we have Nathan's packing rate, we can calculate how many boxes he can pack in an 8-hour shift:
$$ \text{Total boxes} = \text{Rate} \times \text{Total hours} = 12.5 \text{ boxes/hour} \times 8 \text{ hours} = 100 \text{ boxes} $$
Nathan can pack 100 boxes in an 8-hour shift.
More Information
Nathan's efficiency is key to understanding his packing capability. If he can maintain packing at the same rate throughout the shift, his total output over longer hours can easily be calculated. This method of breaking down rates is useful in various real-world scenarios, such as production line work.
Tips
One common mistake is forgetting to divide the total boxes by the total hours to find the correct packing rate. It's important to ensure the rate is calculated properly before using it to find the total number of boxes packed.
