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
The fish pond in the park has an inlet pipe and a drain.
With only the inlet open, the empty pond fills in 8 hours; with only the drain open, the full pond empties in 12 hours.
Each pipe always runs at the same rate.
One day the pond is empty and someone opens both pipes at once.
After how many hours is the pond exactly full?
Show the hints (2)
💡Hint 1: Each hour, how much more water comes in than goes out?
💡Hint 2: Call a full pond some number of parts — the lowest common multiple of 8 and 12, so each pipe moves a whole number of parts an hour. How many parts an hour does each pipe move?
Worked solution
Have a go first, then read the solution step by step.
1.Call a full pond 24 parts (the lowest common multiple of 8 and 12).
2.The inlet adds 24 ÷ 8 = 3 parts an hour; the drain removes 24 ÷ 12 = 2 parts.
3.Each hour 3 come in and 2 go out: a net gain of 3 − 2 = 1 part.
4.How many lots of 1 make 24? 24 ÷ 1 = 24 hours.
⚠️Common mistake: 12 − 8 = 4 hours. It is the amounts per hour that subtract, not the times.
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