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A robot is expected to filter pollution out of at least 350 liters of air and water. It filters air at the rate of 50 liters per minute, and it filters water at the rate of 20 liters per minute.
Write an inequality that represents the number of minutes the robot should filter air
(A) and water
(W) to meet this expectation.

A robot is expected to filter pollution out of at least $350$ liters of air and water. It filters air at the rate of $50$ liters per minute, and it filters water at the rate of $20$ liters per minute. $\newline$ Write an inequality that represents the number of minutes the robot should filter air $(A)$ and water $(W)$ to meet this expectation.

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Modeling with linear inequalities

Full solution

Q. A robot is expected to filter pollution out of at least

350

liters of air and water. It filters air at the rate of

50

liters per minute, and it filters water at the rate of

20

liters per minute.

\newline

Write an inequality that represents the number of minutes the robot should filter air

(A)

and water

(W)

to meet this expectation.

Define Rates: Let's denote the number of minutes the robot filters air as $A$ and the number of minutes it filters water as $W$ . The robot filters air at a rate of $50$ liters per minute and water at a rate of $20$ liters per minute. To find the total volume filtered, we multiply the rate of filtering by the time spent on each task.
Calculate Air Volume: For air, the total volume filtered is $50 \, \text{l} \text{iters}/\text{minute} \times A \, \text{minutes}$ , which equals $50A \, \text{l} \text{iters}$ .
Calculate Water Volume: For water, the total volume filtered is $20 \, \text{liters/minute} \times W \, \text{minutes}$ , which equals $20W \, \text{liters}$ .
Set Total Expectation: The robot is expected to filter at least $350$ liters of air and water combined. This means the sum of the air and water filtered should be greater than or equal to $350$ liters.
Formulate Inequality: We can write this expectation as an inequality: $50A + 20W \geq 350$ .
Meet Filtration Condition: This inequality represents the condition that the robot must meet or exceed in terms of the minutes spent filtering air and water to achieve the expected filtration volume.

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