8
algebra

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

B

Before 20 minutes

C

After 10 minutes

D

Never

Correct Answer: A

Choice A is the correct answer. Set up an inequality for "Tank 1 < Tank 2".

  1. Tank 1 Volume: 500−20m500 - 20m
  2. Tank 2 Volume: 300−10m300 - 10m
  3. Inequality: 500−20m<300−10m500 - 20m < 300 - 10m
  4. Add 20m: 500<300+10m500 < 300 + 10m
  5. Subtract 300: 200<10m200 < 10m
  6. Divide by 10: 20<m20 < m, or m>20m > 20
  7. Interpretation: The time must be greater than 20 minutes.

Wait, "After 20 minutes" implies m>20m > 20. Let's check the options. Option A says "After 20 minutes", which matches m>20m > 20. Option B says "Before", which is m<20m < 20.

?�� 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: T1=300, T2=200, so T1 > T2. Choice D is incorrect because the lines intersect at m=20.

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Linear Functions Set 69