A compound measure combines two quantities into a rate. The two you'll meet most are:

Since both are proportional relationships, you must be comfortable rearranging each one to solve for any of the three variables (e.g. $\text{Distance} = \text{Speed}\times\text{Time}$, $\text{Time} = \text{Distance}\div\text{Speed}$).

The usual complication is time conversion: 50 minutes is not 0.8 hours. Convert using $\div60$: $50\div60 = \tfrac56 \approx 0.833$ hours. Always keep this as an exact fraction or several decimal places until the final step.

Density is not additive — you can't just average two densities. Instead, use the conservation principle: $\text{Total Density} = \dfrac{\text{Total Mass}}{\text{Total Volume}}$.

1. Find the volume of each component separately: $V = M \div D$.
2. Sum the masses to get Total Mass; sum the volumes to get Total Volume.
3. Divide: $\text{Total Density} = \dfrac{\text{Total Mass}}{\text{Total Volume}}$.

Example: Metal A: $1200\text{ g}$ at $5\text{ g/cm}^3$ gives $V_A = 240\text{ cm}^3$. Metal B: $600\text{ g}$ at $3\text{ g/cm}^3$ gives $V_B=200\text{ cm}^3$. Total mass $=1800\text{ g}$, total volume $=440\text{ cm}^3$, so combined density $=1800\div440\approx4.09\text{ g/cm}^3$.

• Speed: to go from km/h to m/s, multiply by 1000 (metres per km) and divide by 3600 (seconds per hour) — equivalent to dividing by $3.6$.
• Density: to go from g/cm³ to kg/m³, multiply by $1000$. This comes from the ratio of the mass conversion factor ($10^{-3}$) to the volume conversion factor ($10^{-6}$, since $1\text{ cm}^3 = 10^{-6}\text{ m}^3$): $10^{-3}\div10^{-6}=10^3=1000$.

Worked Example

A train travels $429\text{ km}$ from City A to City B in 6 hours 39 minutes. Find its average speed in km/h, to 1 d.p.

1. Convert time: $39$ minutes $=\tfrac{39}{60}=0.65$ hours, so total time $=6.65$ hours.
2. Average speed $=429\div6.65\approx64.511$.
3. To 1 d.p.: $64.5\text{ km/h}$.

The gradient of a distance–time graph is the speed, since gradient is itself "change in distance ÷ change in time" — exactly the speed formula. A flat (horizontal) section means the object is stationary; a steeper line means a faster constant speed; a curved section means the speed is changing (accelerating or decelerating). Recognising these features lets you answer "describe the motion" questions directly from the shape of the graph, without needing any further calculation — though if a numerical speed is asked for over a straight section, just calculate rise ÷ run exactly as you would for any gradient.