# Rates

A **rate** is a relationship between two quantities of **different types**. Common examples are:

**Grocery price**- dollars per kilogram ($/kg)**Exercise energy**- kilojoules per minute (kJ/min)**Speed**- kilometres per hour (km/h), metres per second (m/s)

**The word "per" and the slash symbol / mean "divide".**

## Example One - Cost of Strawberries

Strawberries cost $4.50 for 5 kg. What is the price **per** kilogram?

**Answer:**

Price per kilogram = | $4.50 | = $0.90/kg |

5 kg |

## Example Two - Best Buy of Sweets

Which is the better buy of sweets - 5 kilograms of jelly babies for $28.40 or 500 grams of jelly beans for $11.45?

**Answer:**

Jelly babies' price per kg = | $28.40 | = $5.68/kg |

5 kg |

Jelly beans' price per kg = | $11.45 | = $22.90/kg |

0.5 kg |

Jelly babies are cheaper.

## Did You Know This...?

Many sweets, jellies, sauces and medicine capsules contain **Gelatine**, a colourless and flavourless powder extracted from collagen in slaughtered pig hides.
Is that sweet to you?

## Did You Know That...?

If the average frog has a mass of 0.5 kg, less than 0.05 grams of **Fluoride** (more accurately, sodium monofluorophosphate) in toothpaste would kill it.
Do you consider how often you clean your teeth in a year and the possible impact on other living creatures in the environment?

## Questions - Exercise Energy

EXERCISE ENERGY ( kJ / kg / 30 minutes)This is measured in kilojoules of energy burnt for every kilogram of body mass in each ^{1}⁄_{2} hour. | |

Aerobics = 10.6 | Jogging = 17.0 |

Basketball = 20.5 | Mountain-biking = 18.5 |

Canoeing = 6.5 | Swimming = 15.7 |

Dance = 9.2 | Tennis = 14.7 |

Golf = 8.6 | Walking (fast) = 9.3 |

**Q1.** I am 60kg. When I do my favourite exercise for 1 hour, I burn off 780 kilojoules. What sport is this?

**Q2.** Mountain-biking Bob, whose mass is 72 kg, finishes a race in 30 minutes. How much energy did he burn off?

**Q3.** A chocolate bar contains 1722 kilojoules of energy. How long must Tall Tess, a keen lean 56 kg basketball player, play to burn this off?

**Answers**
**A1.** 780 ÷ 60 x 2 = 6.5 Canoeing
**A2.** 1332 kJ
**A3.** 45 minutes

## Maths Fun - World's Heaviest Man

According to the Guinness World Records, the **world's heaviest man** is Manuel Uribe, a Mexican man whose mass is about 600 kg.
If Manuel lost weight at the rate of 10 kg a month, how long would it take for him to become your mass?

## Did You Know That...?

**Brain waves** are electrical impulses within our brains. When we relax, the alpha waves travel between 8 and 12
**Hertz** (between 8 and 12 **waves per second**). When we concentrate, the beta waves travel between 12 and 30 Hertz (between 12 and 30 waves per second).

The **NeuroSky** company has developed a **MindWave headset** that uses brain waves to move objects. The headset and software cost about $100.
One use is for paralysed people to drive wheelchairs. In fact, in 2011, a MindWave headset was used to move a crane with a mass of 56 tonnes.
The Guinness World Record is "**the heaviest machine moved by a brain control interface**".