Question

lydia is comparing the amounts of electricity that different household items use. she reads that her ceiling fan uses 20 kilowatts of energy to run for 8 hours.

1. enter the given rate in the table.

scale up or scale down to answer each question.

1. what is the equivalent rate if lydias fan uses 5 kilowatts of energy?
2. what is the equivalent rate if lydia runs her ceiling fan for 24 hours?
3. what is the equivalent rate if lydias fan uses 160 kilowatts of energy?

Explanation:

Step1: Analyze the rate relationship

We know that the energy consumption rate is constant. The formula for energy \(E = P\times t\) (where \(P\) is power and \(t\) is time).

Step2: Solve for question 1

Given \(E = 20\) kilowatts when \(t = 8\) hours. If \(E = 5\) kilowatts, since \(\frac{20}{5}=4\), then \(t=\frac{8}{4}=2\) hours.

Step3: Solve for question 2

From the proportion \(\frac{20}{8}=\frac{5}{t}\), cross - multiply gives \(20t = 5\times8\), so \(t=\frac{5\times8}{20}=2\) hours.

Step4: Solve for question 3

If \(t = 24\) hours, and the rate \(\frac{P}{t}=\frac{20}{8} = 2.5\). Then \(P=2.5\times24 = 60\) kilowatts.

Step5: Solve for question 4

If \(P = 160\) kilowatts, and the rate \(\frac{P}{t}=\frac{20}{8} = 2.5\). Then \(t=\frac{160}{2.5}=64\) hours.

Answer:

1. \(2\) hours and \(5\) kilowatts
2. \(2\) hours
3. \(60\) kilowatts
4. \(64\) hours