An agricultural drone sprays liquid fertilizer at a constant rate. The drone covers 3 acre… — SAT

An agricultural drone sprays liquid fertilizer at a constant rate. The drone covers $3$ acres of cropland every $20$ minutes. If the drone operates continuously at this rate, how many hours will it take the drone to spray $54$ acres of cropland?

Answer: 6 hours

Answer

The correct answer is 6. Since the drone covers

3

acres every

20

minutes, it covers

9

acres per hour because there are three

20

-minute intervals in one hour (

3 \times 3 = 9

). Dividing the total area of

54

acres by the rate of

9

acres per hour gives

6

hours.

Step-by-Step Solution

Set up a proportion to solve for the total time in minutes,

t

\frac{3}{20} = \frac{54}{t}

Since the drone operates at a constant rate, the ratio of acres to minutes remains constant.

Solve for

t

in minutes.

t = \frac{54 \times 20}{3} = 360

minutes

Cross-multiply and solve for

t

to find the total time needed to cover the cropland.

Convert the total time from minutes to hours.

360 \div 60 = 6

hours

Since

1

hour equals

60

minutes, divide the total minutes by

60

to obtain the final time in hours.

Key Concept

Setting up rates and solving multi-step proportions with unit conversions.

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