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.

Question

Solve this multiple-choice question and choose the correct option.

Curioustab · Accepted Answer

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: 26/(10 + s) = 14/(10 − s)Cross-multiply: 26(10 − s) = 14(10 + s)260 − 26s = 140 + 14s ⇒ 120 = 40s ⇒ s = 3 km/h. 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

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.

Answer

Explanation