Speed, distance and time practice

The three formulas

Conversions: $1$ km $= 1000$ m and $1$ hour $= 60$ minutes $= 3600$ seconds. So $54$ km/h is $54000 \div 3600 = 15$ m/s.

Average speed

Average speed for a round trip is total distance ÷ total time, not the average of the two speeds.

Example: $120$ km out at $20$ km/h and back at $30$ km/h takes $6 + 4 = 10$ hours, so the average speed is $240 \div 10 = 24$ km/h (not $25$).

Meeting, overtaking, trains and rivers

• Meeting: the gap shrinks by the sum of the speeds each minute.
• Catching up: the gap shrinks by the difference of the speeds each minute.
• Trains: to pass through a tunnel or over a bridge, a train travels the tunnel length plus its own length; to pass a pole, just its own length.
• Rivers: upstream speed = still-water speed − current; downstream speed = still-water speed + current.