A company has to make a large number of boxes - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 3

The boxes can be completed in 9 days, so:

• Total machine days needed = $6$ machines * $9$ days = $54$ machine days.
• Machine days used in the first 3 days = $12$.
• Remaining machine days needed = $54 - 12 = 42$ machine days.

For the remaining 6 days, with 6 machines:

• Each day provides 6 machine days, therefore total machine days in 6 days = $6 * 6 = 36$.
• Days needed to reach 42 total remaining machine days = $42 / 6 = 7$ days needed.

Adding up the days:

• Total days from the first 3 days = 3 days
• Additional days needed = 7 days

Thus, total days taken to make all the boxes = $3 + 7 = 10$ days.