GCSE — mathsFoundation1 min read

Speed, Distance, and Time

Calculate speed, distance, and time for GCSE Maths. Solve problems with average speed and unit conversions.

Tutor AI Team
Tutor AI Team

Speed, distance, and time are related by a simple formula. GCSE questions often involve calculating one quantity given the other two, working with different units, and finding average speed.

Core Formula

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Units

  • km/h, m/s, mph
  • km/h → m/s: ÷ 3.6 (or × 518\frac{5}{18})
  • m/s → km/h: × 3.6

Average Speed

Average speed=Total distanceTotal time\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}

Worked Example: Example 1

Problem

A car travels 150 km in 2.5 hours. Speed = 1502.5=60\frac{150}{2.5} = 60 km/h.

Solution

Worked Example: Example 2

Problem

A cyclist rides at 12 km/h for 45 minutes. Distance = 12×0.75=912 \times 0.75 = 9 km.

Solution

Worked Example: Example 3

Problem

Jan drives 100 km at 80 km/h, then 60 km at 40 km/h.

Total distance = 160 km. Total time = 10080+6040=1.25+1.5=2.75\frac{100}{80} + \frac{60}{40} = 1.25 + 1.5 = 2.75 hours.

Average speed = 1602.75≈58.2\frac{160}{2.75} \approx 58.2 km/h.

Solution

Practice Problems

    1. Distance 240 km, time 3 hours. Find speed.
    1. Speed 15 m/s for 2 minutes. Find distance.
    1. Convert 90 km/h to m/s.

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Key Takeaways

  • ✓

    S=DTS = \frac{D}{T}, D=S×TD = S \times T, T=DST = \frac{D}{S}.

  • ✓

    Average speed uses total distance and total time.

  • ✓

    Watch units — convert minutes to hours if using km/h.

Tags:
#gcse#maths#ratio#speed#distance#time

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