In a river, the ratio (speed of stream : speed of a boat in still water) for boat 1 is 2 : 5. For boat 2, the ratio (speed of stream : speed of that boat in still water) is 3 : 4. Find the ratio of the still-water speeds of boat 1 to boat 2.

Introduction / Context:The problem provides ratios of stream speed to each boat’s still-water speed. We are asked for the ratio of the boats’ still-water speeds independent of the actual stream magnitude.

Given Data / Assumptions:

• For boat 1: v_stream / v_b1 = 2 / 5 ⇒ v_b1 = (5/2) v_stream
• For boat 2: v_stream / v_b2 = 3 / 4 ⇒ v_b2 = (4/3) v_stream

Concept / Approach:Express both still-water speeds in terms of v_stream, then take the ratio v_b1 : v_b2 and simplify.

Step-by-Step Solution:

Verification / Alternative check:Choose any v_stream > 0 (e.g., 2). Then v_b1 = 5, v_b2 = 8/3 ⇒ ratio 15:8 holds. The ratio is independent of the actual stream value.

Why Other Options Are Wrong:10:7, 4:3, 5:4 do not equal 15:8 after simplification of the provided ratios.

Common Pitfalls:Inverting the ratios or comparing stream-to-boat directly instead of converting to boat speeds first.

Final Answer:15 : 8.