A hard question on work problems for 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
The school is printing this year's magazine on two copiers, A and B.
Running together, they would finish in 13 hours.
Running A alone for 12 hours and then B alone for 19 hours also finishes the job exactly.
Each copier always prints at the same rate.
How many hours would copier B take to print it all on its own?
Show the hints (3)
💡Hint 1: Compare the two ways: in the second, how many fewer hours does A run, and how many more does B?
💡Hint 2: B's extra time makes up for A's missing time: 1 hour of A = 6 hours of B.
💡Hint 3: So what A prints in 13 hours takes B 78 hours.
Worked solution
Have a go first, then read the solution step by step.
1.Compared with the first way, A runs 13 − 12 = 1 fewer hour and B 19 − 13 = 6 more, with the same result.
2.So 1 hour of A's work = 6 hours of B's.
3.13 hours of A = 6 × 13 ÷ 1 = 78 hours of B.
4.Both together for 13 hours: swap A's 13 hours for 78 hours of B, and B alone takes 78 + 13 = 91 hours.
⚠️Common mistake: answering 19 hours. In the second way A also ran for 12 hours.
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