Set 13: Linear Functions

Explanation

Answer: A

A runner starts at the 10-mile marker and runs toward the finish line at 6 mph. Another runner starts at the 0-mile marker and runs at 8 mph. When does the second runner catch the first?

$5$ hours

✓ Correct

$2$ hours

$4$ hours

$10$ hours

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Relative speed. 1. Runner 1: $d = 6 t + 10$ . 2. Runner 2: $d = 8 t$ . 3. Equate: $8t = 6 t + 10$ . 4. Solve: $2t = 10 \rightarrow t = 5$ . Strategic Tip: Gap (10) divided by Speed Difference (2) = Time (5). Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $5$ hours

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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