Set 8: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. Let $b$ = boat speed in still water and $c$ = current speed. Analysis: - Downstream speed = $b + c$ (current helps) - Upstream speed = $b - c$ (current opposes) - Distance = Speed × Time Step 1: Set up the system: $\begin{cases} (b + c) \cdot 3 = 48 \\ (b - c) \cdot 4 = 48 \end{cases}$ Step 2: Simplify: $\begin{cases} b + c = 16 \\ b - c = 12 \end{cases}$ Step 3: Add the equations: 2b = 28$b = 14$$ Step 4: Find $c$: 14+ c = 16c = 2$$ Solution: Current speed is 2 mph Verification: Downstream: (14 + 2) \times 3 = 48$✓, Upstream:$(14 - 2) \times 4 = 48$✓ Strategic Tip: Current problems: downstream = boat + current, upstream = boat - current. Choice A is incorrect because with$c = 1$: upstream speed would be$(15) \times 4 = 60 \neq 48$. Choice C is incorrect because with$c = 3$: downstream speed would be$(13) \times 3 = 39 \neq 48$. Choice D is incorrect because with$c = 4$: upstream speed would be$(12) \times 4 = 48$✓ but downstream would be$(16) \times 3 = 48$.