6
algebra

A swimmer swims 6 miles downstream in a river in 1 hour. The return upstream takes 2 hours. What is the river's current speed?

A

1 mph

B

1.5 mph

C

2 mph

D

2.5 mph

Correct Answer: B

Choice B is the correct answer. Let ss = swimmer speed in still water and cc = current speed.

System: {(s+c)1=6(sc)2=6\begin{cases} (s + c) \cdot 1 = 6 \\ (s - c) \cdot 2 = 6 \end{cases}

Step 1: Simplify: {s+c=6sc=3\begin{cases} s + c = 6 \\ s - c = 3 \end{cases}

Step 2: Add equations: 2s=92s = 9s=4.5s = 4.5

Step 3: Find cc: 4.5+c=64.5 + c = 6c=1.5c = 1.5

Solution: Current is 1.5 mph

Verification: Down: (4.5+1.5)×1=6(4.5 + 1.5) \times 1 = 6 ✓, Up: (4.51.5)×2=6(4.5 - 1.5) \times 2 = 6

💡 Strategic Tip: Current aids downstream, opposes upstream.

**Other choices fail verification.