Linking speed, time and distance for journeys and races
Distance, speed and time are linked by distance = speed × time, which can be rearranged to find any one of them. Units must match: to change km/h into m/s multiply by 5/18, and to change m/s into km/h multiply by 18/5, so 72 km/h is 20 m/s. Average speed is total distance divided by total time, not the average of the speeds. If you travel equal distances at 40 km/h and 60 km/h, the average speed is 2 × 40 × 60 ÷ (40 + 60) = 48 km/h rather than 50 km/h.
Relative speed handles two moving objects. When they move in opposite directions their speeds add, and when they move in the same direction their speeds subtract. A train passing a pole covers its own length, while a train passing a platform or another train covers the sum of both lengths. For boats and streams, the downstream speed is the boat's speed plus the stream's speed and the upstream speed is their difference, so the boat's speed in still water is half the sum of the downstream and upstream speeds.
Why it matters
These ideas help you plan journeys, estimate arrival times and compare travel options, and they form a large share of the quantitative aptitude section in railway, banking and SSC exams. In physics the same relations become the equations of motion, and relative speed is the starting point for relative velocity in Class 11.
Key terms
- Average speed
- Total distance travelled divided by the total time taken for the whole journey.
- Relative speed
- The speed of one moving object as measured from another moving object.
- Downstream speed
- The speed of a boat moving with the current, equal to its still-water speed plus the stream's speed.
- Upstream speed
- The speed of a boat moving against the current, equal to its still-water speed minus the stream's speed.