6
algebra

A boat travels 48 miles downstream in 3 hours. The return trip upstream takes 4 hours. What is the speed of the current?

A

1 mph

B

2 mph

C

3 mph

D

4 mph

Correct Answer: B

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

Analysis:

  • Downstream speed = b+cb + c (current helps)
  • Upstream speed = bcb - c (current opposes)
  • Distance = Speed × Time

Step 1: Set up the system: {(b+c)3=48(bc)4=48\begin{cases} (b + c) \cdot 3 = 48 \\ (b - c) \cdot 4 = 48 \end{cases}

Step 2: Simplify: {b+c=16bc=12\begin{cases} b + c = 16 \\ b - c = 12 \end{cases}

Step 3: Add the equations: 2b=282b = 28b=14b = 14

Step 4: Find cc: 14+c=1614 + c = 16c=2c = 2

Solution: Current speed is 2 mph

Verification: Downstream: (14+2)×3=48(14 + 2) \times 3 = 48 ✓, Upstream: (142)×4=48(14 - 2) \times 4 = 48

💡 Strategic Tip: Current problems: downstream = boat + current, upstream = boat - current.

Choice A is incorrect because with c=1c = 1: upstream speed would be (15)×4=60 eq48(15) \times 4 = 60 \ eq 48.

Choice C is incorrect because with c=3c = 3: downstream speed would be (13)×3=39 eq48(13) \times 3 = 39 \ eq 48.

Choice D is incorrect because with c=4c = 4: upstream speed would be (12)×4=48(12) \times 4 = 48 ✓ but downstream would be (16)×3=48(16) \times 3 = 48.