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Difficulty: EasyRatios, Rates, and Proportions

A solar panel generates 120120 watt-hours of electricity every 33 hours. At this rate, how many watt-hours of electricity will the solar panel generate in 88 hours?

Answer: 320 watt-hours

Answer

The solar panel will generate 320320 watt-hours of electricity in 88 hours.
To find the total electricity generated, we determine the unit rate of energy generation: 120 watt-hours3 hours=40\frac{120 \text{ watt-hours}}{3 \text{ hours}} = 40 watt-hours per hour. Multiplying this rate by the new duration of 88 hours gives 40×8=32040 \times 8 = 320 watt-hours. Proportional reasoning also works: 1203=x8\frac{120}{3} = \frac{x}{8}, which yields x=320x = 320.

Step-by-Step Solution

1
Calculate the hourly rate of electricity generation.
The rate is 4040 watt-hours per hour.
Dividing the energy produced (120120 watt-hours) by the elapsed time (33 hours) gives the unit rate.
2
Calculate the total energy generated over the new duration of 88 hours.
The total energy is 320320 watt-hours.
Multiplying the unit rate (4040 watt-hours per hour) by the target duration (88 hours) gives the total energy generated.

Key Concept

Calculating and applying unit rates to solve proportional relationships.

Alternative Method

Set up a proportion where the ratio of energy to time remains constant: 1203=x8\frac{120}{3} = \frac{x}{8}. Cross-multiply to solve for xx: 3x=120×83x = 120 \times 8, which simplifies to 3x=9603x = 960. Divide by 33 to find x=320x = 320.
Estimated Time:45s
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Topics

Ratios, Rates, and Proportions

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