Speed, Distance, and Time

Learn

Using the relationship speed = distance ÷ time to solve for any of the three quantities.

For motion at constant speed, the three quantities distance d, speed v, and time t are linked by d = v · t, from which v = d / t and t = d / v. When speed changes over different legs of a trip, the overall average speed is total distance divided by total time (not a plain average of the individual speeds). Units must be consistent across all three quantities — if distance is in kilometres and time in hours, speed is in km/h.

d = v · t; v = d / t; t = d / v; average speed = total distance / total time

• A car travelling 60 km in 1.5 h has speed 40 km/h
• Walking 5 km at 4 km/h takes 1.25 h (1 h 15 min)
• Leg 1: 30 km at 60 km/h (0.5 h); Leg 2: 30 km at 30 km/h (1.0 h) → average = 60 km / 1.5 h = 40 km/h

How to recognize it

• The problem mentions distance, speed, time, or any two of them
• You are asked to find the unknown third quantity
• Multi-leg trips require total distance and total time for the average speed

Common mistakes

• Averaging speeds directly across different-length legs
• Mixing units (km + miles, hours + minutes)
• Computing v = t / d instead of d / t

Practice guidance

Numerical Reasoning