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.
![Rate](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fbbc627b2-1b67-4427-b780-4f0178df3e0f-file.png&w=1920&q=75)
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.
![Hourly rate](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Ffef7f5d9-6d1e-490d-ab57-d86f7f4f1be0-file.png&w=640&q=75)
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:
Weekly Earnings=Hourly Rate×Hours WorkedWeekly Earnings=£12×35=£420Therefore, 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.
![Currency exchange rate](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fabee65c7-20cc-4b18-ab8c-ffaf7502cfab-file.png&w=1080&q=75)
Example:
Question: If £1 is equivalent to 1.30,howmanydollarswillyougetfor£500?</p><p><strong>Solution:</strong></p><ul><li><strong>ExchangeRate:</strong>£1=1.30
To find the equivalent in dollars:
Dollars=Pounds×Exchange RateDollars=£500×1.30=650Thus, you will get 650for£500.</p><h2id="flow−rates"><strong>FlowRates</strong></h2><p>Flowratesareusedtomeasurethevolumeoffluidthatmovesthroughapointorareaperunittime.Thisconceptiswidelyusedinfieldssuchaschemistryandengineering.</p><imgsrc="https://tutorchase−production.s3.eu−west−2.amazonaws.com/26c8c9f4−cb1b−4c96−8bb3−812047ca3806−file.png"alt="Flowratesillustration"style="width:500px;height:201px"width="500"height="201"><p>Imagecourtesyof<ahref="https://www.gigacalculator.com/calculators/pipe−flow−rate−calculator.php">GigaCalculator</a><br></p><h3><strong>Example:</strong></h3><p><strong>Question:</strong>Ifwaterflowsthroughapipeatarateof3litresperminute,howmuchwaterwillflowthroughthepipein2hours?</p><p><strong>Solution:</strong></p><ul><li><strong>FlowRate:</strong>3litres/minute</li><li><strong>Time:</strong>2hours=120minutes(since1hour=60minutes)</li></ul><p>Tocalculatethevolumeofwater:</p>\text{Volume} = \text{Flow Rate} \times \text{Time}<p></p>\text{Volume} = 3 \times 120 = 360 \text{ litres}<p></p><p>Therefore,360litresofwaterwillflowthroughthepipein2hours.</p><h2id="fuel−consumption"><strong>FuelConsumption</strong></h2><p>Fuelconsumptionmeasurestheamountoffuelusedbyavehicleperunitdistance,oftenlitresper100kilometres(l/100km)ormilespergallon(mpg).</p><imgsrc="https://tutorchase−production.s3.eu−west−2.amazonaws.com/d53a34c4−5b75−472b−a992−47a78f4a4f3d−file.png"alt="FuelConsumptionillustration"style="width:500px;height:318px"width="500"height="318"><p>Imagecourtesyof<ahref="https://www.wikihow.com/Calculate−Fuel−Consumption">WikiHow</a></p><h3><strong>Example:</strong></h3><p><strong>Question:</strong>Acarhasafuelconsumptionrateof5litresper100kilometres.Howmuchfuelwillitconsumeoveradistanceof300kilometres?</p><p><strong>Solution:</strong></p><ul><li><strong>FuelConsumptionRate:</strong>5l/100km</li><li><strong>Distance:</strong>300km</li></ul><p>Tocalculatethefuelconsumption:</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.