Telegraphs to Marathons: Unpacking Ratios and Rates

Whether you’re mixing ingredients for the perfect smoothie or checking your split times on a run, ratios and rates sneak into every part of our day. Ratios let us compare quantities – like two cups of flour to one of sugar – while rates compare those quantities across different units, such as kilometres per hour on your bike computer. In this post, we’ll dive into the surprising link between 19th-century telegraph fees and modern marathon paces to see why ratios and rates are more than textbook jargon.

Where did this come from?

Ratios trace back to ancient Greece, where mathematicians like Euclid used them to compare lengths and areas in geometry. The word itself stems from the Latin ratio, meaning “reason” or “reckoning.” Fast-forward to the 1840s, and telegraph companies in Europe began charging customers by the word – one of the first instances of a rate in the modern sense. Later, 19th-century railways posted speed limits in miles per hour, cementing the idea of comparing distance and time.

Where you’ll see this in real life

• Cooking and Baking: Recipe ratios (like 3:1 oil to vinegar) keep flavours balanced. • Scale Models and Maps: Map scales (1:50,000) shrink real distances so you can plan a hike. • Fitness Tracking: Your pace – minutes per kilometre – is a rate that measures performance. • Data Plans and Internet Speeds: Mobile carriers sell data by gigabytes and advertise download speeds in megabits per second; that’s a rate of data per time.

A common misconception

One slip-up students make is mixing up ratios and rates, since both show comparisons. Remember: a ratio is dimensionless – it’s a pure comparison (like 2:1). A rate includes units and tells you how one quantity changes relative to another (like dollars per hour or pages per minute). Always check your units: if they differ, you’re dealing with a rate.