4

Set 12: Linear Inequalities (Intermediate)

Explanation

Answer: A

A tank holds 500 gallons of water and is draining at a rate of 20 gallons per minute. A second tank holds 300 gallons and is draining at 10 gallons per minute. When will the first tank have less water than the second tank?

A.

After 20 minutes

✓ Correct
B.

Before 20 minutes

C.

After 10 minutes

D.

Never

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Set up an inequality for "Tank 1 < Tank 2". 1. Tank 1 Volume: 500−20m500- 20 m 2. Tank 2 Volume: 300−10m300- 10 m 3. Inequality: 500−20m<300−10m500- 20 m < 300 - 10 m 4. Add 20 m: 500<300+10m500< 300 + 10 m 5. Subtract 300: 200<10m200< 10 m 6. Divide by 10: 20<m20< m, or m>20m > 20 7. Interpretation: The time must be greater than 20 minutes. Strategic Tip: Draining means subtraction (negative slope). Choice B is incorrect because it represents the time when Tank 1 has MORE water. Choice C is incorrect because at 10 mins: T 1=300, T 2=200, so T 1 > T 2. Choice D is incorrect because the lines intersect at m=20.

Key Steps:

•

The correct answer is After 20 minutes

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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