Motion Problems: Meeting, Pursuit and River Currents

1. 1The green car gets a head startBy 08:00, the green car has traveled for 1 hour at 30 km/h, covering 30 km. The gold segment now spans only the road that is left.30 × 1 = 30 km
2. 290 km remainWhen the purple car leaves at 08:00, subtract the green car’s 30 km head start from the full 120 km.120 − 30 = 90 km
3. 3Add the closing speedsWatch the two arrows join tip to tail: in one hour the green car covers 30 km and the purple car adds 60 km more, so the gap shrinks by 90 km every hour.30 + 60 = 90 km/h
4. 4Find the time to meetThe remaining 90 km is closed at 90 km/h, so take the gap and divide by the sum of the speeds.90 ÷ 90 = 1 h
5. 5Both cars runWatch the gold segment count down to zero as the two cars run toward each other and the clock rolls toward the meeting time.90 → 0 km
6. 6They meet at 09:001 hour after 08:00, both cars meet 60 km from station A and 60 km from station B.08:00 + 1 h = 09:00
7. 7Check the AnswerAdd the two trails on the road itself: the green car travelled 60 km in all, the purple car 60 km. Together they must rebuild the whole 120 km route.60 + 60 = 120 km ✓
8. 8Wrap-up: add or subtract the speeds?One pair of problems, two signs: moving toward each other, the gap closes by the sum of the speeds; moving in the same direction, only by the difference. When a new problem arrives, ask yourself: are the two cars moving in the same direction or toward each other? What gives it away?Toward each other → ADD · Same direction → SUBTRACT

Change the numbers and watch the diagram redraw itself: