The pattern
Same time, same distance
Two travellers spend the same time, or cover the same distance.
Two people travel, or two workers work, and one thing between them is identical: the time they both spend, or the distance they both cover. Once that shared quantity is pinned down, everything else splits into a fixed ratio. A gap in distance closes at the difference of their speeds.
How to spot it
Two travellers set off together or one chases another, with constant speeds and a question about who is ahead, when they meet, or how far apart they are.
Common mistake
Children divide the whole distance by the difference in speed instead of dividing the gap between the travellers, or compare distances covered over different lengths of time.
12 worked solutions
Standard
- Aladdin and Jasmine — the magic carpet race Aladdin and Jasmine were having a race on their magic flying carpets. They left the same starting point for the market at 13 00. B…
- Bus and car — the catch-up A bus left Town X at 8:00 am travelling at 60 km/h. A car left the same town at 9:00 am travelling in the same direction at 90 km/…
- Drone race — X and Y to the rooftop Drone X and Drone Y raced from the same depot to deliver packages to a rooftop pad. Both launched at 10:00 and did not change thei…
- Race cars — Car A and Car B Two remote-control race cars, Car A and Car B, started from the same line on a track at 14:00. Both did not change their speed thr…
- Speedboats — the Dolphin and the Marlin race to an island Two speedboats, the Dolphin and the Marlin, raced from the same jetty to an island. Both left at 08:00 and did not change their sp…
- Two trains — leaving in opposite directions Two trains leave the same station in opposite directions. One travels at 70 km/h and the other at 90 km/h. How far apart are they …
Challenging
- Cycling race — Mei and Lin Mei and Lin took part in a cycling race. Mei cycled at a speed of 20 km/h. Both of them did not change their speed throughout the …
- Ice-cream stalls — Stall A and Stall B At a school fair, Stall A and Stall B both scoop ice-cream cups for customers. Stall A scoops 4 more cups per minute than Stall B.…
- Printing machines Printing machines
- Priya and Wei Ming wrap sweets by hand at a candy factory. Priya wraps 5 more sweets per minute than Wei Ming. They start wrapping together, and after 48 minutes Priya leaves for her break …
- PSLE 2012 — Bakery and library A bakery and a library are 120 m apart. They are located between Hong's house and Jeya's house. The bakery is exactly half-way bet…
- Two tanks — same flow rate, equal height Two rectangular tanks are shown below. At first, Tank A was empty and one third of Tank B was filled with water. Both taps were tu…
4 more that use it
Filed under a different pattern, but this one is part of the working.
- Two workers — finishing a job together Filed under Number × value
- Two pipes — filling a tank together Filed under Number × value
- Roller-skating race — Kai and Mia Filed under Units and parts
- Kayaking race — Ben and Farah Filed under Units and parts
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.