Using and Comparing Rates

Interesting choices. What’s the best way to compare two options?

To compare these properly, we need something called a unit rate. The word unit just means one. A unit rate tells you how much for just one — one hour, one kilometre, one minute. $15 per hour is a unit rate — it’s how much for one hour. 75 km/h is a unit rate — it’s how far in one hour. The reason unit rates are useful — once everything is per one, you can compare directly. You can’t easily compare $45 for 3 hours with $70 for 5 hours — the hours are different. But you can compare $15 per hour with $14 per hour.

And once you know the unit rate, you can use it to calculate any amount — just multiply.

If someone earns $20 per hour, how much do they earn in 5 hours? Each hour they earn $20, so 5 hours is 5 lots of $20 — that’s $100.

A car travels 35 km every hour. How far does it go in 3 hours? 3 lots of 35 — that’s 105 km.

Now let’s go back to our Would You Rather questions and use unit rates to find out what’s better.

Walking dogs pays $48 for 3 hours. How much is that per hour? We want the amount for just one hour, so we divide. $48 divided by 3 equals $16 per hour. Quick check: 3 lots of $16 makes $48. That checks out. Now picking up dog poop — $75 for 5 hours. Same thing — divide by the number of hours. $75 divided by 5 equals $15 per hour. So walking dogs actually pays more per hour — $16 versus $15.

The train travels 360 km in 5 hours. To find the speed, divide. 360 divided by 5 equals 72 km per hour. Now what about the ferry?

The ferry is actually faster — 75 km/h versus 72 km/h. Even though the train covers more distance, it takes longer to do it.

The snail moves 90 cm in 2 minutes. 90 divided by 2 equals 45 cm per minute. Now grab a pen — the tortoise moves 2 metres in 5 minutes. But careful — we need the same units. 2 metres is 200 cm.

The snail is faster! 45 cm per minute versus 40 cm per minute. Who would have guessed?