Overview

The main skill is translation: identify variables, write equations, and keep units consistent. Draw tables for rate and mixture problems.

Key Ideas

• Distance = rate $\times$ time.
• For mixtures, total amount = sum of parts, and total concentration is a weighted average.
• Ratios are easiest to manipulate when written as fractions.

Worked Example

A tank is filled by two pipes. Pipe A fills the tank in $6$ hours, pipe B in $10$ hours. How long together?

Their combined rate is $\frac{1}{6} + \frac{1}{10} = \frac{8}{30} = \frac{4}{15}$ tanks per hour. The time is $\frac{1}{4/15} = \frac{15}{4}$ hours.

Common Pitfalls

• Mixing up rate and time when adding.
• Forgetting that averages are weighted by amounts, not just counts.

Practice Problems