A hard question on tree planting for P4–P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P2 to P5 papers. Sawing logs, striking clocks and lining up lamp posts are all the same problem.
The question
The school hall has a big clock that strikes every hour, as many times as the hour.
The strikes are evenly spaced, and a single strike takes so little time that we ignore it.
At 3 o'clock, from the first strike to the last takes 4 seconds.
One day Ming practises the piano in the hall from 1 o'clock to 6 o'clock and hears every time the clock strikes, including at 1 o'clock and at 6 o'clock.
Adding up, for each hour, the time from its first strike to its last, how many seconds is that?
Show the hints (3)
💡Hint 1: 3 strikes — how many waits are there between them?
💡Hint 2: Find how long one wait is; then count the waits at each hour from 1 to 6.
💡Hint 3: Each wait is 2 s; 1 o'clock has 0 waits, 2 o'clock has 1, … 6 o'clock has 5.
Worked solution
Have a go first, then read the solution step by step.
1.3 strikes have 2 waits between them: 4 ÷ 2 = 2 s each.
2.An hour of n strikes has n − 1 waits. From 1 to 6 o'clock: 0, 1, 2, 3, 4, 5 waits, in all 0 + 1 + 2 + 3 + 4 + 5 = 15.
3.2 s a wait: 15 × 2 = 30 seconds.
⚠️Common mistake: thinking 3 strikes make 3 waits. The waits sit between strikes, so there is one fewer.
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