Rates are a fundamental aspect of our daily lives, providing a way to understand how different quantities relate to each other over time or through other measures. In this section, we will explore common measures of rate, including hourly rates of pay, currency exchange rates, flow rates, and fuel consumption. Each of these measures plays a crucial role in various fields, from economics to engineering, and understanding them is essential for solving real-world problems.

Hourly Rates of Pay

Hourly rates of pay are a common method of compensation in many jobs. This rate determines how much an employee earns per hour of work.

Example:

Question: If an employee earns £12 per hour and works 35 hours in a week, how much will they earn for that week?

Solution:

• Hourly Rate: £12
• Hours Worked: 35 hours

To calculate the weekly earnings:

Therefore, the employee earns £420 for the week.

Currency Exchange Rates

Currency exchange rates show the value of one currency in terms of another. These rates fluctuate based on economic factors and are crucial for international trade and travel.

Example:

Question: If £1 is equivalent to $1.30, how many dollars will you get for £500?</p><p><strong>Solution:</strong></p><ul><li><strong>Exchange Rate:</strong> £1 =$1.30

To find the equivalent in dollars:

Thus, you will get $650 for £500.</p><h2 id="flow-rates"><strong>Flow Rates</strong></h2><p>Flow rates are used to measure the volume of fluid that moves through a point or area per unit time. This concept is widely used in fields such as chemistry and engineering.</p><img src="https://tutorchase-production.s3.eu-west-2.amazonaws.com/26c8c9f4-cb1b-4c96-8bb3-812047ca3806-file.png" alt="Flow rates illustration" style="width: 500px; height: 201px" width="500" height="201"><p>Image courtesy of <a href="https://www.gigacalculator.com/calculators/pipe-flow-rate-calculator.php">Giga Calculator</a><br></p><h3><strong>Example:</strong></h3><p><strong>Question:</strong> If water flows through a pipe at a rate of 3 litres per minute, how much water will flow through the pipe in 2 hours?</p><p><strong>Solution:</strong></p><ul><li><strong>Flow Rate:</strong> 3 litres/minute</li><li><strong>Time:</strong> 2 hours = 120 minutes (since 1 hour = 60 minutes)</li></ul><p>To calculate the volume of water: </p>$\text{Volume} = \text{Flow Rate} \times \text{Time}$<p></p>$\text{Volume} = 3 \times 120 = 360 \text{ litres}$<p></p><p>Therefore, 360 litres of water will flow through the pipe in 2 hours.</p><h2 id="fuel-consumption"><strong>Fuel Consumption</strong></h2><p>Fuel consumption measures the amount of fuel used by a vehicle per unit distance, often litres per 100 kilometres (l/100km) or miles per gallon (mpg).</p><img src="https://tutorchase-production.s3.eu-west-2.amazonaws.com/d53a34c4-5b75-472b-a992-47a78f4a4f3d-file.png" alt="Fuel Consumption illustration" style="width: 500px; height: 318px" width="500" height="318"><p>Image courtesy of <a href="https://www.wikihow.com/Calculate-Fuel-Consumption">WikiHow</a></p><h3><strong>Example:</strong></h3><p><strong>Question:</strong> A car has a fuel consumption rate of 5 litres per 100 kilometres. How much fuel will it consume over a distance of 300 kilometres?</p><p><strong>Solution:</strong></p><ul><li><strong>Fuel Consumption Rate:</strong> 5 l/100km</li><li><strong>Distance:</strong> 300 km</li></ul><p>To calculate the fuel consumption:</p>$\text{Fuel Consumed} = \left( \frac{\text{Distance}}{100} \right) \times \text{Fuel Consumption Rate}$<p></p>$\text{Fuel Consumed} = \left( \frac{300}{100} \right) \times 5 = 15 \text{ litres}$

Thus, the car will consume 15 litres of fuel over 300 kilometres.