Ratios and Rates

Lesson

A rate is a ratio between two measurements with different units. A common example of a rate is speed (which is written in kilometres per hour or km/h). You can see that this describes a relationship between two measurements- kilometres and hours.

However, we can also convert rates into different units of measurement. Doing this is similar to using the unitary method. Let's look at the process using an example: Convert $20$20L/hour into mL/second.

1. We write the rate we are given.

$20$20L/hour

2. Convert the first unit of measurement so it matches one of the units of measurement we need.

$20$20L/hour=$20000$20000mL/hour

3. Multiply or divide both sides of the rate to find the equivalent rate. Remember that the second quantity in a rate is usually expressed as a single unit.

$20000$20000mL/hour | $=$= | $333.33$333.33...mL/min | (Both sides of the rate have been divided by $60$60 to find the rate per minute) |

$=$= | $5.55$5.55...mL/sec | (Again, both sides have been divided by $60$60) | |

$=$= | $5.6$5.6mL/sec (1 d.p.) |

This is similar to solving an equation: whatever you do to one side, you have to do to the other to keep the rates equivalent.

Handy Conversions

$\text{1 metre}=\text{100 centimetres}$1 metre=100 centimetres

$\text{1 metre}=\text{1000 millimetres}$1 metre=1000 millimetres

$\text{1 kilometre}=\text{1000 metres}$1 kilometre=1000 metres

$\text{1 litre}=\text{1000 millilitres}$1 litre=1000 millilitres

$\text{1 hour}=\text{60 minutes}$1 hour=60 minutes

$\text{1 minute}=\text{60 seconds}$1 minute=60 seconds

Convert $1642$1642 ml/hr into ml/min, to the nearest millilitre.

Think: How many minutes are there in an hour?

Do:

There're $60$60 minutes in an hour, so:

$1642$1642ml/hr | $=$= | $1642$1642ml/$60$60min |

$=$= | $\frac{1642}{60}$164260ml/$\frac{60}{60}$6060min | |

$=$= | $\frac{1642}{60}$164260ml/min | |

$=$= | $27$27ml/min rounded |

Assuming that $1$1 AUD can buy $0.97$0.97 USD, how much AUD is equivalent to $25$25 USD? Give the answer correct to the nearest cent.

Think: First find the rate of USD per AUD, or think of how many USDs that can be bought with $1$1 AUD are in $25$25 USD.

Do:

The rate of exchange is $0.97$0.97 USD/AUD, so then:

$0.97$0.97 USD/AUD | $=$= | $\frac{25}{0.97}\times0.97$250.97×0.97 USD/$\frac{25}{0.97}$250.97 AUD |

$=$= | $25$25 USD/$\frac{25}{0.97}$250.97 AUD | |

$=$= | $25$25 USD/$25.77$25.77 AUD rounded |

So $25$25 USD would be equivalent to $25.77$25.77 AUD.

The other method would be to think: $1$1 AUD buys $0.97$0.97 USD, so how many $0.97$0.97 USDs are there in $25$25 USD?

$25\div0.97=25.77$25÷0.97=25.77 AUD, so we get the same answer.

Assuming that $1$1 AUD can buy $0.90$0.90 USD, how many AUD's are equivalent to $24$24 USD?

Round your answer to the nearest penny.

An athlete runs $270$270 m in $27$27 seconds. What is his speed in km/hr?

Convert $600$600km/hr to km/min.