Repeating Events Time Problems Practice Test Worksheets
Repeating events questions ask you to count how many buses, trains, trams, or ferries arrive within a time window. The key is listing each service at its own interval and checking whether the start and end times are included.
For students who can count intervals, but get stuck when repeating events overlap after different cycle lengths.
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The Rules Every Repeating Events Question Uses
Each service has its own rhythm. Count one service at a time, then add the counts together.
⏱️ Rule 1: Start from the shared time
All services arrive or depart together at the stated starting time. Add each interval repeatedly from that time.
Example: Every 8 minutes from 10:00 gives 10:08, 10:16, 10:24, 10:32, and so on.
🚦 Rule 2: Only count times inside the window
Ignore arrivals before the start of the window and after the end of the window.
Example: In 10:30 to 11:15, 10:24 is too early but 10:32 counts.
✅ Rule 3: Inclusive means count the endpoints
If the question says "inclusive", an arrival exactly at the start or end of the window counts.
Example: 10:30 and 11:15 both count in a 10:30 to 11:15 inclusive window.
➕ Rule 4: Add service counts, not unique times
If two services arrive at the same clock time, they are still two arrivals.
Example: If two trains arrive at 11:00, that contributes 2 trains, not 1 time.
3 Worked Repeating Events Examples
One straightforward, one multi-step, and one classic mistake to avoid.
1. Counting One Regular Service
Question: A service arrives every 15 minutes. It starts at 10:00. How many arrivals are there from 10:30 to 11:15, inclusive?
Worked Method
Step 1: List the 15-minute times from 10:00: 10:15, 10:30, 10:45, 11:00, 11:15.
Step 2: Keep the times inside 10:30 to 11:15 inclusive: 10:30, 10:45, 11:00, 11:15.
Answer: 4 arrivals. The endpoints count because the window is inclusive.
2. Adding Several Services
Question: Four bus routes arrive together at Eastside Hub at 4:00pm. Route C arrives every 4 minutes, Route E every 6 minutes, Route H every 10 minutes, and Route I every 20 minutes. How many buses call from 5:00pm to 5:20pm, inclusive?
Worked Method
Route C: 5:00, 5:04, 5:08, 5:12, 5:16, 5:20 = 6 buses.
Route E: 5:00, 5:06, 5:12, 5:18 = 4 buses.
Route H: 5:00, 5:10, 5:20 = 3 buses.
Route I: 5:00, 5:20 = 2 buses.
Total: 6 + 4 + 3 + 2 = 15 buses.
3. Same Time, Different Services
Question: Three trains arrive together at 10:00am. One arrives every 8 minutes, one every 15 minutes, and one every 20 minutes. How many trains pass through from 10:30am to 11:15am, inclusive?
Worked Method
Every 8 minutes: 10:32, 10:40, 10:48, 10:56, 11:04, 11:12 = 6 trains.
Every 15 minutes: 10:30, 10:45, 11:00, 11:15 = 4 trains.
Every 20 minutes: 10:40, 11:00 = 2 trains.
Total: 6 + 4 + 2 = 12 trains.
Tip: Do not merge matching times. At 11:00, two different trains arrive, so both are counted.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Repeating Events pack contains 90 questions across 3 printable test sets. Students practise interval counting, inclusive time windows, schedules, and total arrival counts.
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