6

Set 17: Linear Equations (Intermediate)

Explanation

Answer: D

A pipe fills a tank in 4 hours. Another drains it in 6 hours. If both are open, how long to fill the tank?

A.

5

B.

2

C.

10

D.

12

✓ Correct

Detailed Explanation

Choice D is correct. Choice D is the correct answer. 1. Rates: Fill = 1/41 /4, Drain = 1/6-1/6. 2. Equation: 1416=1t\frac{1}{4} - \frac{1}{6} = \frac{1}{t} 3. Common Denominator (12): 312212=112\frac{3}{12} - \frac{2}{12} = \frac{1}{12} 4. Solve: t=12t = 12 Choice B is incorrect because it results from an error in the solution process. Choice C is incorrect because it results from an error in the solution process. Choice A is incorrect because it results from an error in the solution process.

Key Steps:

The correct answer is 12

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

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