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Speed & Time Comparison Puzzles

Thinking Skills · Y4 OC
Year 4 OC
Lesson Guide
Explanation
Speed puzzles at OC level need no formulas — just one idea: over the SAME distance, going faster shrinks the time by the same factor. Twice as fast, half the time. Four times as fast, a quarter of the time. A typical train question: the slow train takes 6 hours (10 am to 4 pm); the express is three times as fast, so it needs 6 ÷ 3 = 2 hours. Speed multiplies, time divides — that swap is the whole trick.
Your Turn
A walk to the shops takes 40 minutes. Cycling is 4 times as fast. How long by bike? Check: 40 ÷ 4 = 10 minutes.
Watch Out
Don't subtract! 4 times as fast does NOT mean 4 hours less — it means the time is divided by 4.
Explanation
The full puzzle: slow train 10 am to 4 pm; express three times as fast arrives at the same moment — when did it leave? Three small steps. (1) Known journey: 10 am to 4 pm is 6 hours. (2) Scale it: express takes 6 ÷ 3 = 2 hours. (3) Count BACK from the shared arrival: 4:00 pm minus 2 hours = 2:00 pm. Most students stumble on step 3 — they add to the departure instead of subtracting from the arrival. Ask: which clock time do both trains share? Anchor there.
Your Turn
Ferry A: leaves 9 am, arrives noon. Ferry B is 3 times as fast and arrives at noon too. When did B leave? Check: 3 h ÷ 3 = 1 h; noon − 1 h = 11 am.
Watch Out
Anchor on the SHARED time (the arrival), not the slow one's departure. 10 am + 2 h = noon is the trap answer.
Explanation
Race-style puzzles mix departure times AND journey lengths — 'Ana leaves at 2:00 and takes 50 minutes; Ben leaves at 2:20 and takes 25.' Don't compare pieces; convert EVERY traveller to an arrival time. Ana: 2:00 + 50 = 2:50. Ben: 2:20 + 25 = 2:45. Ben wins by 5 minutes despite the later start. Arrival time is the universal currency — head starts, speeds and shortcuts all melt into it. Compute each arrival separately, then just read off the earliest.
Your Turn
Cara leaves at 3:10, takes 35 min. Dev leaves 3:30, takes 10 min. Who arrives first? Check: Cara 3:45, Dev 3:40 — Dev wins.
Watch Out
Crossing an hour boundary is the slip zone: 2:40 + 30 min = 3:10, not 2:70. Hop to the o'clock first.
Explanation
Rate chains: 'a machine fills 6 bottles in 4 minutes' scales in both directions — multiply BOTH numbers by the same factor and the fact stays true. Need 30 bottles? That's 5 lots of 6, so 5 lots of 4 minutes: 20. Given 20 minutes? That's 5 lots of 4, so 30 bottles. Pick the factor that lands exactly on the number in the question. When it doesn't land exactly, drop to ONE first (6 bottles in 4 min → 1 bottle per ⅔ min) — but OC questions almost always pick friendly factors.
Your Turn
3 pizzas cook in 12 minutes (one oven load of 3). How long for 12 pizzas? Check: 12 = 4 × 3 → 4 × 12 = 48 minutes.
Watch Out
Scale BOTH numbers. Doubling the bottles but not the minutes creates a machine twice as fast as the real one.
Explanation
The toolkit: faster DIVIDES time over the same distance; anchor calculations on the time both journeys share; convert every traveller to an arrival time before comparing; and scale rate facts by multiplying both numbers together. Every OC speed question yields to these four moves plus careful clock arithmetic — hop to the o'clock when adding minutes across an hour boundary. No formulas, no algebra. Quiz and exercises!
Your Turn
Capstone: a bus takes 45 min for a route; an express bus is 3× as fast and both arrive at 4:00 pm. When did the express leave? Check: 45 ÷ 3 = 15 min; 4:00 − 15 = 3:45 pm.
Watch Out
Read whether the question wants a DURATION ('how long') or a CLOCK TIME ('when did it leave') — right number, wrong form loses the mark.
📌 Key Points — this lesson in a nutshell
  • Same distance: n times as fast → time divided by n. Never subtract.
  • Shared-arrival puzzles: find the known trip time, scale it, then count BACK from the shared arrival.
  • Races with different starts: convert every traveller to an ARRIVAL TIME, then compare.
  • Rate facts scale: multiply both numbers by the same factor (6 bottles in 4 min → 30 in 20).
  • Hop to the o'clock when adding minutes across an hour: 2:40 + 30 = 3:10.
  • Check whether the answer should be a duration or a clock time.
Step 1: Introduction
Step 1 of 5
Same trip, different speeds Ashby Kelso Slow train: the whole trip takes 6 hours. Express, 3× as fast: takes 6 ÷ 3 = 2 hours. Same distance: twice as fast → HALF the time. Four times as fast → a QUARTER of the time. Speed up = divide the time. No formulas needed — just "faster shrinks the clock".
When did the express leave? Slow train: departs 10:00 am, arrives 4:00 pm. Express: 3× as fast, arrives at the SAME 4:00 pm. When did the express depart? Step 1 — slow trip time: 10 am → 4 pm = 6 hours. (Always find the KNOWN journey first.) Step 2 — express time: 6 ÷ 3 = 2 hours. Same distance, 3× speed → ⅓ time. Step 3 — count BACK from arrival: 4:00 pm − 2 h = 2:00 pm ✓ Arrive together, so subtract the express time from 4 pm. Three small steps: known trip → scaled trip → count back.
Who arrives first? Ana leaves at 2:00 and walks for 50 min. Ben leaves at 2:20 and cycles for 25 min. Ana arrives: 2:00 + 50 min = 2:50 Ben arrives: 2:20 + 25 min = 2:45 ✓ Convert every traveller to an ARRIVAL TIME, then compare. Ben leaves later but still wins by 5 minutes. A head start is minutes, speed is a divider — never compare one person's start with another person's journey length.
Scaling chains A machine fills 6 bottles in 4 minutes. How long for 30 bottles? How many bottles in 20 minutes? 30 bottles = 5 × 6 → 5 × 4 min = 20 min scale both sides together 20 min = 5 × 4 min → 5 × 6 = 30 bottles the chain runs both ways Multiply BOTH numbers by the same factor and the fact stays true. 6-in-4 → 12-in-8 → 30-in-20. Pick the factor that lands on the number the question asks about.
Fast thinking about fast things 🚄 Faster divides time 4× speed → ¼ time, same distance Anchor on shared times count back from a joint arrival Arrival time = currency convert everyone, then compare Scale both sides 6-in-4 → 30-in-20 by ×5 Every answer here is reachable with ÷, ×, and careful clock arithmetic — no formulas, no algebra. Quiz and exercises!
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