Compound Measures
Speed and density are rates: one quantity shared out over another. Their units spell out their formulas, and one cover-up triangle solves all three arrangements of each.
National curriculum KS3: use compound units such as speed, unit pricing and density to solve problems1 · Speed: distance shared by time
Speed says how much distance fits into each unit of time. The triangle holds the three formulas at once: cover the one you want and read what is left. D on top, S and T below.
Units carry the formula. "km/h" literally reads "kilometres divided by hours" — the unit tells you speed = distance ÷ time. The same works for density (g/cm³) and pressure (N/m²).
2 · Density: mass packed into space
Density is how much mass is squeezed into each cm³. Same triangle, new letters: M on top, Density and Volume below.
3 · Watch the time units
Most lost marks here are time slips: minutes used as hours. 150 km in 90 minutes is not 150 ÷ 90 — convert first: 90 min = 1.5 h, speed = 100 km/h.
Worked examples
A car travels 210 km in 3 hours. Find its average speed.
A cyclist rides at 24 km/h for 45 minutes. How far?
A metal block has mass 890 g and volume 100 cm³. Its density?
Quick check
What you've learned
Speed = distance ÷ time; density = mass ÷ volume — the units (km/h, g/cm³) say so. In the triangle, cover what you want: top ÷ bottom, or bottom × bottom. Convert time to the right unit before calculating: 45 minutes is 0.75 hours, never 0.45. A density below 1 g/cm³ floats in water; above 1 sinks.