A solar power facility operates two types of solar panel arrays: Array Alpha and Array Bet… — GRE General Test

A solar power facility operates two types of solar panel arrays: Array Alpha and Array Beta. When operational, Array Beta produces electricity at a constant hourly rate that is $25\%$ greater than the constant hourly rate of Array Alpha. On a clear day, Array Alpha operated for $8$ hours and Array Beta operated for $6$ hours, together generating a total of $3,100$ kilowatt-hours (kWh) of electricity. What was the hourly production rate of Array Alpha, in kWh per hour?

A
160
B
193.75
200Answer
D
248
E
250

Answer

200 kWh per hour

Let the hourly rate of Array Alpha be

r

kWh per hour. Since Array Beta produces at a rate

25\%

greater, its hourly rate is

1.25r

kWh per hour. Multiply each rate by the respective number of hours operated: Array Alpha produced

8r

kWh and Array Beta produced

6 \times 1.25r = 7.5r

kWh. Combining these gives

8r + 7.5r = 15.5r = 3,100

. Solving for

r

yields

r = 200

kWh per hour.

Step-by-Step Solution

Define variables for the hourly rates of Array Alpha and Array Beta.

Let

r

be the hourly rate of Array Alpha in kWh per hour. Since Array Beta's rate is

25\%

greater, Array Beta's rate is

r + 0.25r = 1.25r

kWh per hour.

Establishing the linear relationship between the two unknown rates.

Set up the total electricity output equation using rate times time for each array.

\text{Total Energy} = (8 \text{ hours} \times r) + (6 \text{ hours} \times 1.25r) = 3,100

Total production is the sum of production from Array Alpha and Array Beta.

Simplify the algebraic equation and solve for

r

8r + 7.5r = 3,100 \implies 15.5r = 3,100 \implies r = \frac{3,100}{15.5} = 200

Isolating

r

gives the hourly rate of Array Alpha.

Key Concept

Linear Algebraic Modeling of Combined Rates and Percentages

Estimated Time:1m 30s

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