Boat and River Current

1. 1Downstream: Stack the ArrowsGoing with the flow, the current's arrow stacks head-to-tail onto the boat's arrow. The stacked-on piece is exactly 4 km/h long.20 + 4 = ? km/h
2. 2Two Arrows Merge into OneThe two arrows slide together and merge into a single gold arrow: the downstream speed is 24 km/h. No third arrow is drawn — the gold arrow IS the two arrows added together.20 + 4 = 24 km/h
3. 3Onto the BoardThe numbers fly up to the board from the arrows themselves: 20 from the still-water label, 4 from the current arrow's head, 24 from the head of the gold arrow they merged into.20 + 4 = 24 km/h
4. 4Upstream: The Same Arrows Come BackThe boat turns home. The current's arrow — the very same one — travels down to the return row and stacks behind the boat's tail, exactly as it did downstream. Watch it in the next steps.20 + 4 = 24 km/h
5. 5Merge Again — Then the Current SlidesThe two arrows merge into the gold 24 km/h arrow on this row too. But the current's arrow does not dissolve this time: it slides back over the boat's tail and waits there.20 + 4 = 24 km/h
6. 6The Current Turns AroundZooming into the return row: the current's arrow flips a full 180°. Still the same 4 km/h current, but now it points straight at the boat — from a push to a resistance.4 km/h — against the boat
7. 7The Part That Gets EatenThe tail marked in red is the part that is lost: the current's contribution flips from +4 to −4, so the gold arrow loses 8 km/h and shrinks to 16 km/h — the real upstream speed.20 − 4 = 16 km/h
8. 8Onto the Board: The Second RowThe board's second row assembles from tokens on the return row: 20 from the boat's arrow, 4 from the head of the turned-around current, 16 from the head of the shrunken gold arrow.20 − 4 = 16 km/h
9. 9What That Means in DistanceThe clock counts 2 hours: the boat covers 24 × 2 = 48 km downstream, but only 16 × 2 = 32 km upstream on the 60 km route. The distance labels appear only after both bars have finished growing.48 km vs 32 km in 2 h
10. 10Check Backwards, on the ArrowsRecover the hidden numbers from the two real speeds: (24 + 16) ÷ 2 = 20 — the boat's own speed, confirmed by the still-water arrow blinking. And (24 − 16) ÷ 2 = 4 — the current, confirmed by the current's arrow blinking.24 − 16 = 8; 24 + 16 = 40
11. 11Summary — and the Reverse QuestionBoth gold arrows stay on their rows, the board holds both calculations, and the turned-around current lies dimmed above. One last question: downstream 24 km/h, upstream 16 km/h — how fast is the current? Try to work it out before looking back at the check step.Downstream add, upstream subtract — the current always counts.

Change the numbers to test the engine with any sum & difference problem: