6
algebra

A kayak travels 18 miles downstream in 1.5 hours. The upstream return takes 3 hours. What is the current speed?

A

2 mph

B

3 mph

C

4 mph

D

5 mph

Correct Answer: B

Choice B is the correct answer. Let kk = kayak speed, cc = current speed.

System: {(k+c)1.5=18(kc)3=18\begin{cases} (k + c) \cdot 1.5 = 18 \\ (k - c) \cdot 3 = 18 \end{cases}

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

Step 2: Add: 2k=182k = 18k=9k = 9

Step 3: Find c: 9+c=129 + c = 12c=3c = 3

Solution: Current is 3 mph

Verification: Down: (9+3)×1.5=18(9+3) \times 1.5 = 18 ✓, Up: (93)×3=18(9-3) \times 3 = 18

💡 Strategic Tip: Current helps or hinders depending on direction.