11.06 Identify and compare rates

A carton of 10 eggs cost \$6.50. How much does 1 egg cost?

An athlete runs 270\text{ m} in 27 seconds. What is his speed in \text{ km/hr}?

A 0.75 litre bottle of milk costs \$1.05. How much does the milk cost per litre?

A 1.35\text{ kg} packet of mince costs \$15. How many grams of mince does each dollar buy?

In an ice cream eating contest, the winner ate 2.22 litres of ice cream in 2 minutes.

What was the winner's rate of consumption of ice-cream in \text{ mL/s}?

Which two of the following rates are equivalent?

• Rate A: Writing 34 words per second

• Rate B: Writing 68 words in 30 seconds

• Rate C: Writing 714 words in 21 minutes

• Rate D: Writing 816 words per hour

• Rate E: Writing 34 words per minute

Convert 80 \text{ m/s} to \text{km/hr} by solving the following:

Convert:

Brendon feels like buying some ice-cream for himself and his friends. He considers the following offers:

• A box of 8 Cornettos costs \$18.00

• A box of 5 Magnums costs \$7.25

For each of the following, determine which item is better value:

A supermarket sells two different brands of eggs, Happy Hens and Sunny Side Up.

• Happy Hens eggs cost \$6.00 for 12 eggs

• Sunny Side Up eggs cost \$1.50 for 5 eggs

James needs 1\text{ kg} of blueberries to make a pie. He made a list of the prices of blueberries at four supermarkets close to his house:

• Market Fresh: 1\text{ kg} for \$3

• Garden Fresh: 500\text{ g} for \$2.25

• Fruit World: 2\text{ kg} for \$5.50

• My Market: 2\text{ kg} for \$6

Which shop was selling blueberries at the cheapest price per kilogram?

Isabelle is buying juice for her nephew's birthday party. She considers the following offers:

• A 3.2\text{ L} bottle of apple juice costs \$13.76

• A 2.1\text{ L} bottle of orange juice costs \$6.30

Lisa has never made a potato salad before and wants to try making one. She has to choose between two types of potatoes at the store:

• A 10.275 \text{ kg} sack of sebago potatoes costs \$13.70

• A 7.7 \text{ kg} sack of russet potatoes costs \$14.00

Sally is deciding which of two different cereals she should buy:

• Choco Pops costs \$0.84 for 200 grams

• Special Q costs \$0.36 for 100 grams

Consider the following scenarios:

• Han paid \$124.62 for 67\text{ L} of petrol in Humbleton.

• Amelia paid \$82.08 for 57\text{ L} of petrol in Dunkilderry.

Fiona wants to buy some salmon from Whole-sail Seafood.

• A 1.9\text{ kg} Atlantic salmon costs \$31.35.

• A 2\text{ kg} Tasmanian salmon costs \$51.00.

Consider the following scenarios:

• At Emporio, durian is sold for 76 cents per kilogram.

• At Greenery, each 5.5\text{ kg} durian is sold for \$2.97.

Consider the sale prices of the following apartments:

• A 200\text{ m}^2 apartment is sold for \$440\,000.

• An adjacent apartment that is 220\text{ m}^2 in size is sold for \$440\,000.

Lisa is trying to save money so she deposits \$3.20 into her bank account for every 8 coffees she purchases. How much does Lisa deposit for each cup of coffee?

Maria ran for 4 hours at the speed of 10\text{ km/h} .

A car is travelling at 26\text{ m/s}. How many kilometres does it travel in 1 hour?

A car travels 520.2\text{ km} in 10 hours and 12 minutes. Calculate the car's average speed for the trip.

Michael is driving his car. He knows how far he has travelled in kilometres, and how long it has taken him in minutes. Determine whether the following rates can be used to calculate his average speed:

A child is weighed on their first birthday to find that they have gained 9.855 kilograms since they were born.

Marie cycles 77 kilometres in 7 hours on her bike. Determine whether the following journeys would have an equivalent speed to Marie's.

A crabeater seal can filter 0.975 litres of water in each dive looking for food. They can stay under water for 39 minutes each dive.

The earth’s surface receives energy from the sun at a rate of 1.296 \text{ kW/m} ^2. Consider that1000\text{ J/sec}= 1\text{ kW} and 1055\text{ J}= 1\text{ BTU} (British Thermal Unit):

The speed limit on a particular road in the US is 70 miles per hour. An Australian visiting the country is more familiar with the speeds using the unit \text{km/h}.

Kilimanjaro, the tallest mountain in Africa, is 20322\text{ ft} high. Note that 1\text{ ft}= 0.3048\text{ m}.

Patricia eats 7.2 litres of ice cream in 6 minutes in an ice-cream eating contest. Find Patricia's rate of ice-cream consumption in millilitres per second.

A teacher can mark F exams per hour. If they mark N exams in T hours, express T in terms of F and N.

Tectonic plates are large segments of the earth’s crust that move slowly. The image below shows the 15 major plates in the world:

Suppose that the Carribean plate moves 4.8\text{ cm} per year.