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
An estate needs a long corridor painted.
Mr Chan alone would finish it in 10 days;
Mr Lee alone would take 15 days.
Each works at a steady pace every day.
If they work on it together from the first day, how many days will it take?
Show the hints (2)
💡Hint 1: Pick a number that both 10 and 15 divide into, and split the whole job into that many equal parts.
💡Hint 2: With the job as 30 parts, how many parts does each man do a day?
Worked solution
Have a go first, then read the solution step by step.
1.Call the whole job 30 parts (the lowest common multiple of 10 and 15).
2.Mr Chan does the 30 parts in 10 days: 30 ÷ 10 = 3 a day. Mr Lee takes 15 days: 30 ÷ 15 = 2 a day.
3.Together they do 3 + 2 = 5 parts a day.
4.How many lots of 5 make 30? 30 ÷ 5 = 6 days.
⚠️Common mistake: answering 10 + 15 = 25 days. Two working together must be quicker than either alone.
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