# SAT Math Multiple Choice Question 390: Answer and Explanation

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**Question: 390**

**15.**

The equation shown above represents the following scenario: A chemical laboratory uses two air purifiers to clean the air of contaminants emitted while working with hazardous materials. One is an older model, and the other is a new model that is considerably more energy efficient. The new model can clean the air of contaminants three times as quickly as the older model. Working together, the two air purifiers can clean the air in the lab in 7 hours. Which of the following describes what the term in the equation represents?

- A. The portion of the air the new model can clean in 1 hour
- B. The portion of the air the older model can clean in 1 hour
- C. The time it takes the older model to clean the air by itself
- D. The time it takes the older model to clean of the air by itself

**Correct Answer:** B

**Explanation:**

B

Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Strategic Advice: Think of the rate given in the question in terms of the constant term you see on the right-hand side of the equation. Working together, the two air purifiers can clean the air in 7 hours. This is equivalent to saying that they can clean of the air in 1 hour.

Getting to the Answer: If is the portion of the air the two purifiers can clean together in 1 hour, then each term on the left side of the equation represents the portion that each purifier can clean individually in one hour. Since the new model is 3 times as fast as the older model, represents the portion of the air the new model can clean in 1 hour, and represents the portion of the air the older model can clean in 1 hour.