A volunteer packs boxes for a charity - OCR - GCSE Maths - Question 8 - 2023 - Paper 5

To determine if the volunteer can pack 55 boxes in less than 9 minutes, we will first calculate the time taken to pack 5 boxes and then scale that to find the time for 55 boxes.

1. Calculate time for one box:

   The time taken to pack 5 boxes is 45 seconds. Therefore, the time taken to pack one box is:

   $ext{Time per box} = \frac{45 \text{ seconds}}{5 \text{ boxes}} = 9 \text{ seconds per box}$

2. Calculate time for 55 boxes:

   To find the time taken to pack 55 boxes, we multiply the time per box by the number of boxes:

   $ext{Time for 55 boxes} = 55 \text{ boxes} \times 9 \text{ seconds per box} = 495 \text{ seconds}$

3. Convert time to minutes:

   We convert seconds into minutes:

   $495 \text{ seconds} = \frac{495}{60} \text{ minutes} = 8.25 \text{ minutes}$

Since 8.25 minutes is less than 9 minutes, we have shown that they can pack 55 boxes in less than 9 minutes.