Rates and Unit Rates

A rate compares two quantities with different units. Examples: 60 miles per hour, $3.50 per gallon, 200 words per minute. A unit rate has a denominator of 1: [formula] Example: If you drive 150 miles in 3 hours, your unit rate (speed) is frac{150}{3} = 50 miles per hour.

Example: A factory produces 840 widgets in 12 hours. What is the production rate in widgets per hour?

The key formula is: [formula] This rearranges to: - text{Rate} = frac{text{Quantity}}{text{Time}} - text{Time} = frac{text{Quantity}}{text{Rate}} For combined rates (two workers doing the same job), add the rates: [formula]

Example: Pipe A fills a pool in 6 hours. Pipe B fills it in 4 hours. How long does it take both pipes together?