🏁

Catch-Up Track

Distance gap divided by speed gap

Run two racers on the same track and watch the distance gap shrink by the speed difference. The chase ends when the faster runner has eaten the whole starting gap.

What this game shows · Pursuit Race Track

A pursuit problem has two moving objects going the same direction. This game keeps both racers moving while a gap meter shrinks, so students can see why the relevant rate is the speed difference, not either speed alone.

Starting gap
the distance the faster runner must close.
Speed difference
fast speed minus slow speed; the amount of gap removed per time unit.
Catch time
starting gap divided by speed difference.

Aligned with CCSS 6.RP.A.2 and 6.RP.A.3 for unit rate and rate reasoning.

Relative speed

Catch-Up Track

Two racers move in the same direction. The only thing that closes the gap is the speed difference.

Catch time6.4s
Launch the chaseSet the gap and speeds, then run both racers on the same track.
Fast runnerSlow runner starts 32m ahead
catchguess
Fast
Slow
Remaining gap32.0
32 / (9 - 4) = 6.4The faster runner eats the starting gap by the speed difference each second.

Olympiad thinking model

Who this demo helps, and where to practice next

Catch-Up Track is built for students who need a visual way to decode multi-step puzzle structure. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.

Catch-Up Track helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.

Learning goals

  • In same-direction pursuit, both objects keep moving, but only the speed difference closes the gap.
  • Catch time equals starting distance gap divided by speed gap.
  • Changing either the gap or the speed difference changes the catch time immediately.

How to play

  1. 1 Fix one quantity and watch which quantity changes.
  2. 2 Write the hidden relationship in words before writing an equation.
  3. 3 Use the related grade topics to transfer the puzzle move into standard word problems.
FAQ

Pursuit problems, animated.

01 Why do pursuit problems use speed difference? Relative speed

Because both objects move in the same direction. The slower object also moves forward, so only fast speed minus slow speed closes the gap.

02 What is the catch-up formula? gap / speed gap

Catch time = starting distance gap / (fast speed - slow speed). The game shows that as the shrinking gap meter.

03 How does the prediction marker help? Predict

Students drop a marker before running the race, then compare it to the real catch point. The error is spatial, not just numeric.

04 Which grade is this for? Grades 5-6

Grades 5-6, especially Grade 6 ratio and unit-rate reasoning.

Related Fun Math games