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4.03 Rates in the home

Worksheet
Rates in the home
1

Express each of the following in watts.

a

582 joules per second

b

An appliance consuming 658 joules in 1 second.

c

An appliance consuming 14\,280 joules over 17 seconds.

2

An appliance consumes energy at a rate of 1800 watts. How many joules of energy does it use if it runs for 12 seconds?

3

An appliance consumes energy at a rate of 1200 watts. How many joules of energy does it use if it runs for 29 seconds?

4

An appliance consumes energy at a rate of 900 watts. How many joules of energy does it use if it runs for 28 seconds?

5

4.7\text{ kWh} of energy is used by an appliance over a 10 hour period. What is its power in kilowatts?

6

An appliance consumes energy at a rate of 0.38\text{ kW} for 4 hours. How much energy is this in kilowatt hours?

7

An appliance consumes energy at a rate of 0.44\text{ kW}. If the appliance consumes 2.64\text{ kWh}, how long is the appliance in use?

8

The air conditioner in a house consumes 2.1\text{ kWh} of energy in a day. If the average cost of electricity is \$0.11\text{/kWh}, what is the running cost of the air conditioner for a single day?

9

The fridge in a house consumes 2.8\text{ kWh} of energy in a day. If electricity costs \$0.14\text{/kWh}, what is the running cost of the fridge for a single day?

10

A fridge consumes energy at a rate of 210 watts. The fridge remains on 365 days a year. Given that electricity costs \$0.12\text{/kWh}, what is the running cost of the fridge for an entire year?

11

An office microwave consumes energy at a rate of 1100 watts. The microwave runs for 2 hours a day and electricity costs \$0.13\text{/kWh}.

What is the average running cost of a microwave for a single day?

12

Amy is looking to purchase a new coffee machine for the office. She is deciding between two models that cost the same, the 1050-watt Cuppa Joe brand and the 800-watt Java Juicer brand. The coffee machines will be on for approximately 0.6 hours a day. The average rate for electricity is \$0.17 per\text{ kWh}. Given that there are 365 days in a year:

a

Calculate the yearly running cost of the Cuppa Joe brand coffee machine.

b

Calculate the yearly running cost of the Java Juicer brand coffee machine.

c

Given that both models perform the same, which of the two brands should Amy choose?

13

A household wants to find the cost of running their appliances in the kitchen. The appliances, the amount of watts consumed, and the amount of time they are active in a day are given in the table below. The average cost of electricity is \$0.15\text{/kWh}.

AppliancePower Required (watts)Time Active (hours)
\text{Toaster}12000.2
\text{Kettle}19000.5
\text{Light globe}908

What is the combined running cost of the appliances in one day?

14

A household wants to calculate the running cost of their fan and electric heater. The 65-watt heater is on for 900 hours in a year, while the 950-watt fan is on for 630 hours a year. The cost of electricity is \$0.17\text{/kWh}.

What is the running cost of heating and cooling for a year?

15

Tobias needs a new washing machine. He is deciding between two models that cost the same, the Washington brand and the Loaded brand. The washing machines both use different amounts of power depending on the selected cycle. The length and power required for each cycle are given in the table below. Tobias knows he performs around 80 washes and spins each year, and the average cost of electricity is \$0.13\text{/kWh}.

\text{Washington}\text{Loaded}
\text{Cycle}\text{Power (Watt)}\text{Time (Hour)}\text{Power (Watt)}\text{Time (Hour)}
\text{Wash}2000.47000.2
\text{Spin}3100.48000.025
a

Calculate the yearly running cost of the Washington appliance.

b

Calculate the yearly running cost of the Loaded appliance.

c

If Tobias wants to save on running costs, which of the two brands should he choose?

16

Mohamad is upgrading all 11 light globes in his house to energy saving globes. His current globes are 75-watt and the energy saving globes are 9-watt. Each globe will be used for approximately 1150 hours a year. The average cost of electricity is \$0.16\text{/kWh}.

a

Calculate the yearly running cost of the original light globes in the house.

b

Calculate the yearly running cost of the energy saving light globes.

c

How much will Mohamad save each year on lighting costs after he makes the switch to energy saving globes?

17

A television is used for 5 hours a day, 365 days a year and consumes energy at a rate of 240 watts. Electricity costs \$0.16\text{/kWh}.

a

Calculate the yearly running cost of the television.

b

If the television is only used for 0.5 hours a day, how much money would be saved each year?

18

Mario and Tricia are comparing the running costs of their heaters. Mario’s heater requires 710 watts and takes 1.6 hours to heat his living room. Tricia’s heater requires 1110 watts, but it takes only 0.6 hours to heat her living room. The rooms are the same size and they pay the same price for electricity, which is \$0.15\text{/kWh}.

a

Whose heater is the most cost efficient in heating their rooms?

b

Mario heats up the room 103 times a year and Tricia heats up the room 191 times a year. Who has the cheaper yearly running cost?

19

Lachlan is looking to buy a new dishwasher for his restaurant. His two options are the 2400watt Power Clean brand for \$850 and the 1100 watt Sparkle Sparkle brand for \$1350. The dishwasher will be used for approximately 6 hours a day, 365 days a year. The average cost of electricity is \$0.16\text{/kWh}.

a

Calculate the yearly running cost of the Power Clean dishwasher.

b

Calculate the yearly running cost of the Sparkle Sparkle dishwasher.

c

How much would Lachlan save each year in running costs by purchasing the more expensive Sparkle Sparkle model?

d

Lachlan purchases the more expensive Sparkle Sparkle brand. How long will it take for the savings in running costs to make up the extra cost of the Sparkle Sparkle dishwasher? Round your answer in years to two decimal places.

20

Xanthe uses a 165 watt computer for 0.5 hours each day, 365 days a year. Noah uses a 75 watt model for 11 hours each day, 200 days a year. The cost of electricity is \$0.17\text{/kWh}.

a

Calculate the yearly running cost of Xanthe’s computer.

b

Calculate the yearly running cost of Noah’s computer.

c

Xanthe wants to purchase the same computer as Noah and continue to use it the same amount of time. Would she save or lose money on running costs?

d

Xanthe purchases the same computer model as Noah for \$235 more than she is able to sell her own computer. How long will it take for the yearly energy savings to cover the extra cost of the new laptop?

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Outcomes

MS2-12-3

interprets the results of measurements and calculations and makes judgements about their reasonableness, including the degree of accuracy and the conversion of units where appropriate

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