Rates:

RATES:A rate is a ratio that compares quantities measured in different units. For example, the speed of a car is measured in km/h (kilometres per hour).

The ‘per’ symbol (/) is also a form of division.

Rates may be calculated by dividing the two quantities measured.

Example #1:

What is the average speed of a car that travelled 360km in 4 hours?

Average speed (km/h)= 360km / 4h= 360 divided by 4= 90km/h

Example #2:

What is the run rate of a one-day cricket team that scored 300 runs in 50 overs?

Run rate (runs/over)= 300 runs / 50 overs= 300 divided by 50= 6 runs/over

Converting Units of Measurement:

Some rate problems will involve different units of measurement.

Remember, when solving rate problems all RATIOS must be in PROPORTION (equal measurements).

COMMON UNITS:

mm-cm-m-km10mm=1cm100cm=1m1000m=1km

ml-L1000ml=1L

g-kg 1000g=1kg

sec-mins-hours60secs=1 minute3600secs=1 hour

1.Solve these problems involving rates:

a)What is the average speed of a train that travelled 600km in 3 hours?

b)What is the cost per minute of an 8 minutes phone call costing $2.40?

c)Mr James ran 26 kilometres in 2 and a half hours. How fast did he run per hour? How fast did he run per minute?

PRACTICE PROBLEMS:

2. Solve these problems involving rates:a)What is the cost per metre of 7m of rope that costs

$21?

b)A driver takes 10 hours to travel from Sydney to Melbourne. What is the average speed for this 880km trip?

c) The UAE needs 81 runs in the next 9 overs to win a one-day cricket match. What run rate is required?

d)The 1400km plane ride from Sharjah to Egypt takes 3 hours. What is the average speed of the aircraft?

e)A patient’s heart beats 360 times in 5 minutes. What is the patient’s heart rate in beats per minute?

f) A 20 litre can of paint costs $80. What is the cost per litre?

g)A taxi driver paid $90 for 60L of fuel. What is the cost per litre?