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".
| 
| 
|