A boat moves 26 km downstream and 14 km upstream in the same time. If its still-water speed is 10 km/h, find the stream speed.

Introduction / Context:Equal-time conditions convert distance/speed statements into a solvable equation for the stream speed s when still-water speed b is known.

Given Data / Assumptions:

• Still-water speed b = 10 km/h.
• Downstream distance = 26 km; upstream distance = 14 km.
• Times equal.

Concept / Approach:Downstream speed = b + s; upstream speed = b − s. Set 26/(b + s) = 14/(b − s) and solve for s.

Step-by-Step Solution:

Verification / Alternative check:Times: 26/13 = 2 h and 14/7 = 2 h (equal).

Why Other Options Are Wrong:2 or 2.5 km/h do not equalize the travel times.

Common Pitfalls:Adding times instead of equating them, or using distance difference.

Final Answer:3 km/h