Time, Speed & Distance • Topic 2 of 4

Average & Relative Speed

Average speed over equal distances is the harmonic mean 2ab/(a+b), not the arithmetic mean. Relative speed: two bodies moving in the same direction close the gap at (a - b); moving toward each other they meet at (a + b). Use relative speed for two trains/cars meeting or overtaking, and for two people on a track.

✅ Solved examples

1. Go 60 km/h, return 40 km/h (same road). Average speed?
2x60x40/(60+40) = 4800/100 = 48 km/h.
2. Two cars 90 km apart move toward each other at 40 and 50 km/h. Time to meet?
Relative speed 90 km/h; time = 90/90 = 1 hour.
3. A train at 60 km/h overtakes a man walking at 6 km/h in the same direction. Closing speed?
60 - 6 = 54 km/h.
4. Two runners start together same direction at 8 and 5 km/h on a 6 km loop. When does the faster lap the slower?
Gap grows at 3 km/h; one full lap (6 km) gap in 6/3 = 2 hours.

✏️ Practice — try these, take hints as needed

1. Up 30, down 60. Average speed?
2ab/(a+b).
2x30x60/90.
—
40 km/h
2. 120 km apart, toward each other at 50 and 70. Meet in?
Rel speed 120.
120/120.
—
1 hour
3. Chasing: 72 and 60 km/h. Closing speed?
Same direction subtract.
72 - 60.
—
12 km/h
4. Average of 45 and 55 km/h over equal legs?
2x45x55/100.
4950/100.
—
49.5 km/h
5. Two cars opposite, 40 and 60, 200 km apart. Meet in?
Rel 100.
200/100.
—
2 hours

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
← Speed, Time & Distance Trains →