A solar energy storage system collects electricity from two solar panel arrays, Array X an… — SAT

A solar energy storage system collects electricity from two solar panel arrays, Array $X$ and Array $Y$ . Array $X$ produces $3$ kilowatt-hours (kWh) of electricity for every $4$ hours of direct sunlight. Array $Y$ produces $5$ kWh of electricity for every $6$ hours of direct sunlight. If both arrays receive direct sunlight simultaneously, how many hours of direct sunlight are required for the two arrays to produce a combined total of $38$ kWh of electricity?

Cevap: 24 hours

Cevap

The correct answer is

24

. First, find the rate of each array in kWh per hour: Array

X

has a rate of

\frac{3}{4}

kWh/hour and Array

Y

has a rate of

\frac{5}{6}

kWh/hour. Since the arrays operate simultaneously, add their individual rates to find the combined rate of

\frac{3}{4} + \frac{5}{6} = \frac{9}{12} + \frac{10}{12} = \frac{19}{12}

kWh/hour. To find the total hours

t

needed to produce

38

kWh, set up the equation

\frac{19}{12}t = 38

. Solving for

t

gives

t = 38 \times \frac{12}{19} = 24

hours.

Adım Adım Çözüm

Calculate the individual hourly rates of electricity production for Array

X

and Array

Y

Array

X

produces at a rate of

\frac{3}{4}

kWh per hour, and Array

Y

produces at a rate of

\frac{5}{6}

kWh per hour.

Converting the given production rates to unit rates (kWh per hour) allows them to be directly compared and combined.

Add the individual rates to find the combined rate of both arrays operating simultaneously.

Combined rate is

\frac{19}{12}

kWh per hour.

Since both arrays operate simultaneously, their rates of production add together. The common denominator for

4

and

6

12

, so

\frac{3}{4} + \frac{5}{6} = \frac{9}{12} + \frac{10}{12} = \frac{19}{12}

Determine the time required to produce a combined total of

38

kWh.

24

hours.

Divide the total target production of

38

kWh by the combined rate of

\frac{19}{12}

kWh per hour:

38 \div \frac{19}{12} = 38 \times \frac{12}{19} = 2 \times 12 = 24

Anahtar Kavram

Ratios, Rates, and Proportions

Tahmini Süre:1m 30s

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