What it does
Distance, speed and time are linked by distance = speed × time. For one runner that is a simple sum. The interesting puzzles have two: when does a faster runner catch one with a head start, and where do two people walking towards each other meet? Both are solved with the relative speed: how fast the gap between them closes.
This page puts runners A and B on a straight track:
- Same way, B has a head start: A gains on B at A’s speed minus B’s speed, so the catch-up time is head start ÷ (vA − vB).
- Towards each other: the gap closes at A’s speed plus B’s speed, so the meeting time is track length ÷ (vA + vB).
Press Play (or drag the time slider) to watch the race. A distance-time graph draws both runners as lines; where the lines cross they are at the same place at the same time, and a red dot marks it.
It fits Class 8 Mathematics, proportional reasoning (time, speed and distance, where distance is in direct proportion to time and time in inverse proportion to speed), and leads into motion in Class 9 Science. Direct and inverse proportion are drawn in the proportion grapher; graphs of one moving object are in motion graphs live.
How to use it
- Choose Same way or Towards each other, and type the track length in metres.
- Set the speeds of A and B in m/s with the sliders or boxes. The steps show each speed in km/h too.
- For the same-way race, set h, B’s head start in metres.
- Play runs the whole race in about six seconds; Pause stops it; the t slider moves to any moment. The line under it gives both positions and the gap.
A worked example
The page starts with a 400 m track, A at 8 m/s, B at 6 m/s with a 40 m head start.
- 8 m/s = 8 × 3.6 = 28.8 km/h and 6 m/s = 21.6 km/h.
- A finishes in 400 ÷ 8 = 50 s; B has 360 m to run and takes 60 s.
- A gains 8 − 6 = 2 m every second, and must close 40 m.
- They meet after 40 ÷ 2 = 20 s, when A has run 8 × 20 = 160 m.
Towards each other on a 600 m track at 7 and 5 m/s: the gap closes at 12 m/s, so they meet after 600 ÷ 12 = 50 s, 350 m from A’s start.
Check yourself
Four fresh questions each time: a speed from distance and time, km/h to m/s, a catch-up time and a meeting time. Type the answer and press Check. Nothing is saved.
FAQ
Why multiply by 3.6 to go from m/s to km/h? 1 m/s is 3600 m in an hour, which is 3.6 km in an hour.
What if A is not faster? Then the gap never closes and the two lines on the graph never cross. If A is faster but B reaches the finish first, they do not meet on the track either.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- Distance = speed × time, the change between m/s and km/h, and relative speed for catching up and meeting are standard school mathematics and physics. Wording, pictures and examples are fibub's own.
- Checked against hand-worked examples (40 m head start, 8 m/s against 6 m/s: caught after 20 s at 160 m; 600 m apart at 7 and 5 m/s: meet after 50 s).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.