Speed< > to change
Math · 15 · Problem-Solving and Data Analysis

Rates and Unit Conversion

Notes

Key points

  • Write units on every number; cancel them like fractions.
  • Multiply by factors equal to 1: 60 min1 h\tfrac{60\ \text{min}}{1\ \text{h}}.
  • Squared units convert twice: 1 ft2=144 in21\ \text{ft}^2=144\ \text{in}^2; cubed, three times.
  • Density = mass ÷ volume; population density = people ÷ area.
  • Average speed = total distance ÷ total time, not the average of speeds.
  • Work rates add: together 1a+1b\tfrac{1}{a}+\tfrac{1}{b} jobs per hour.

Formulas

Distanced=rtd=rt
Unit chain5 m/s×3600 s1 h=18,000 m/h5\ \text{m/s}\times\dfrac{3600\ \text{s}}{1\ \text{h}}=18{,}000\ \text{m/h}
Densityρ=mV\rho=\dfrac{m}{V}
Average speedvˉ=total distancetotal time\bar{v}=\dfrac{\text{total distance}}{\text{total time}}
Combined work1a+1b=1t\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{t}t = time working together

Common traps

  • Converting area with a linear factor: 1 yd2=9 ft21\ \text{yd}^2=9\ \text{ft}^2, not 3.
  • Averaging two speeds when the times differ.
  • Flipping a conversion factor so the units multiply instead of cancel.

SAT tip

Build the unit chain before the arithmetic. If the units cancel to what's asked, the setup is right.

Test yourself

10 official SAT questions on Rates and Unit Conversion, easiest first.

    Next lesson16 · Statistics