Rates

What is a Rate?

A rate is a measure that shows how one quantity changes in relation to another quantity. Rates compare two different types of measurements.

For example:

• Speed compares distance to time (how far you travel in a certain time)
• Price compares cost to quantity (how much you pay for each item)
• Fuel consumption compares distance to fuel used (how far you can travel on a certain amount of fuel)

Rates are usually written using the word "per" or using a forward slash (/). For example:

• 60 kilometres per hour = 60 km/h
• 5 dollars per kilogram = $5/kg
• 30 metres per second = 30 m/s

Common Measures of Rate

1. Hourly Rates of Pay

An hourly rate of pay tells you how much money someone earns for each hour they work.

Formula: Pay = Hourly rate × Number of hours worked

Example: If someone earns $12 per hour and works for 8 hours, their total pay is: Pay =$12 × 8 =$96

Finding the hourly rate: If you know the total pay and hours worked, you can find the hourly rate: Hourly rate = Total pay ÷ Number of hours worked

Example: A person earns $240 for working 15 hours. Hourly rate =$240 ÷ 15 =$16 per hour

2. Exchange Rates Between Currencies

An exchange rate tells you how much of one currency you can get for another currency. Different countries use different currencies (like dollars, pounds, euros, yen).

Example: If the exchange rate is 1 USD = 0.85 EUR, this means:

• For every 1 US dollar, you get 0.85 euros

Converting currencies: To convert from one currency to another, multiply by the exchange rate.

Example: Convert $200 USD to EUR if the rate is 1 USD = 0.85 EUR: 200 × 0.85 = 170 EUR

Going the other way: If you want to convert euros back to dollars, divide instead: If you have 170 EUR and 1 USD = 0.85 EUR: 170 ÷ 0.85 = 200 USD

3. Flow Rates

A flow rate measures how much liquid (or gas) flows through a pipe or container in a certain amount of time.

Formula: Flow rate = Volume ÷ Time

Common units: litres per minute (L/min), cubic metres per second (m³/s)

Example: A tap fills a 20-litre bucket in 4 minutes. Flow rate = 20 ÷ 4 = 5 litres per minute

Finding volume or time:

• Volume = Flow rate × Time
• Time = Volume ÷ Flow rate

Example: If water flows at 8 litres per minute, how long does it take to fill a 100-litre tank? Time = 100 ÷ 8 = 12.5 minutes