An agricultural drone sprays liquid fertilizer at a rate of 1.5 fluid ounces per square ya… — SAT

An agricultural drone sprays liquid fertilizer at a rate of $1.5$ fluid ounces per square yard. The drone travels at a constant speed of $4.5$ miles per hour, spraying a continuous path that is exactly $6$ feet wide. Which of the following is closest to the rate at which the drone sprays the fertilizer, in gallons per minute? (Given that $1\text{ mile} = 5,280\text{ feet}$ , $1\text{ yard} = 3\text{ feet}$ , and $1\text{ gallon} = 128\text{ fluid ounces}$ )

3.09Answer
B
3.58
C
9.28
D
27.84

Answer

The rate of

3.09

gallons per minute is closest to the drone's fertilizer spraying rate.

The correct answer is

3.09

because converting the speed of

4.5

miles per hour gives

396

feet per minute. Multiplying this by the width of

6

feet results in

2,376

square feet per minute. Dividing this by

9

converts the rate to

264

square yards per minute. Multiplying by the spray density of

1.5

fluid ounces per square yard gives

396

fluid ounces per minute. Finally, dividing by

128

fluid ounces per gallon yields approximately

3.09

gallons per minute.

Step-by-Step Solution

Convert the speed of the drone from miles per hour to feet per minute.

4.5\text{ miles/hour} = 396\text{ feet/minute}

To find the rate of area covered per minute, the speed must first be expressed in feet per minute. Multiply

4.5

5,280

to convert to feet per hour, then divide by

60

to convert to feet per minute:

\frac{4.5 \times 5,280}{60} = 396

Calculate the area covered by the drone per minute in square feet.

396\text{ feet/minute} \times 6\text{ feet} = 2,376\text{ square feet/minute}

Multiplying the travel speed in feet per minute by the path width of

6

feet gives the area covered per minute in square feet.

Convert the area rate from square feet per minute to square yards per minute.

2,376\text{ square feet/minute} \div 9 = 264\text{ square yards/minute}

Since

1\text{ yard} = 3\text{ feet}

, a square yard is

3 \times 3 = 9

square feet. Therefore, divide the area in square feet by

9

to convert to square yards.

Determine the fertilizer spray rate in fluid ounces per minute.

264\text{ square yards/minute} \times 1.5\text{ fluid ounces/square yard} = 396\text{ fluid ounces/minute}

Multiplying the area covered per minute by the spray density yields the volume of fertilizer sprayed per minute.

Convert the spray rate from fluid ounces per minute to gallons per minute.

396\text{ fluid ounces/minute} \div 128 \approx 3.09\text{ gallons/minute}

Since

1\text{ gallon} = 128\text{ fluid ounces}

, divide the fluid ounces per minute by

128

to find the rate in gallons per minute.

Key Concept

Unit conversions involving compound rates and area scaling.

Estimated Time:3m 0s

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