Set 6: Systems of Equations

Choice B is correct. Choice B is the correct answer. Let $p$ = plane speed in still air and $w$ = wind speed. System: Distance = Speed × Time $\begin{cases} (p + w) \cdot 2 = 600 \\ (p - w) \cdot 3 = 600 \end{cases}$ Step 1: Simplify: $\begin{cases} p + w = 300 \\ p - w = 200 \end{cases}$ Step 2: Add equations: 2p = 500$p = 250$$ Step 3: Find $w$: 250+ w = 300w = 50$$ Solution: Wind speed is 50 mph Verification: With wind: (250 + 50) \times 2 = 600$✓, Against:$(250 - 50) \times 3 = 600$✓ Strategic Tip: Wind/current helps in one direction, opposes in the other. Choice A is incorrect because with$w = 40: plane speed would be 260, and return trip would be $$220\times 3 = 660 \neq 600$$. Choice C is incorrect because with w = 60: plane speed would be 240, and return trip would be $$180\times 3 = 540 \neq 600$$. Choice D is incorrect because with w = 75$: plane speed would be 225, and return trip would be $150\times 3 = 450 \neq 600$.