A medium question on work problems for P4–P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P3 to P6 papers; harder ones have someone leaving partway, people taking turns, or cows grazing a field that keeps growing.
The question
Before term starts, a printing works prints exercise books on its presses.
4 presses running together for 2 hours turn out 80 exercise books.
Every machine makes the same number an hour.
How many hours would 9 presses take to make 450 exercise books?
Show the hints (2)
💡Hint 1: First find how many books one machine makes in one hour.
💡Hint 2: With 9 machines, how many books an hour?
Worked solution
Have a go first, then read the solution step by step.
1.One machine makes 80 ÷ 4 = 20 books in 2 hours.
2.One machine makes 20 ÷ 2 = 10 books an hour.
3.9 machines make 10 × 9 = 90 books an hour.
4.How many lots of 90 make 450? 450 ÷ 90 = 5 hours.
⚠️Common mistake: scaling the time by the number of machines only, or by the amount only. Both change.
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