6
algebra

A canoe travels 24 miles downstream in 2 hours. The return upstream takes 4 hours. Find the speed of the canoe in still water.

A

8 mph

B

9 mph

C

10 mph

D

12 mph

Correct Answer: B

Choice B is the correct answer. Let cc = canoe speed in still water and rr = river current speed.

System: {(c+r)2=24(cr)4=24\begin{cases} (c + r) \cdot 2 = 24 \\ (c - r) \cdot 4 = 24 \end{cases}

Step 1: Simplify: {c+r=12cr=6\begin{cases} c + r = 12 \\ c - r = 6 \end{cases}

Step 2: Add equations: 2c=182c = 18c=9c = 9

Solution: Canoe speed is 9 mph in still water

Verification: Downstream: (9+3)×2=24(9+3) \times 2 = 24 ✓, Upstream: (93)×4=24(9-3) \times 4 = 24

💡 Strategic Tip: Current helps downstream, opposes upstream.

**Other choices fail verification.