The time taken by a boat to go 34 km upstream is 25% more than the time it takes to go 40 km downstream. If the speed of the stream is 4 km/h, then what is the speed (in km/h) of the boat in still water?

Explanation

Given:D 1 = 34 km D 2 = 40 km Speed of stream (u) = 4 km/h T 1 = 1.25 × T 2 Formula used:Time = Distance/Speed When boat go upstream, Relative speed = v - u When boat go downstream, Relative speed = v + u Where, v = speed of boat in still water Calculation:When boat go upstream, Time (T 1) = Distance (D 1)/Speed (v - u) T 1 = 34/(v - u) .......(i) When boat go downstream, Time (T 2) = Distance (D 2)/Speed (v + u) T 2 = 40/(v + u) ......(ii) According to question, ⇒ 34/(v - u) = 1.25 × 40/(v + u) ⇒ 34v + 136 = 50v - 200 ⇒ 16v = 336 ⇒ v = 21 km/h ∴ Speed of the boat in still water is 21 km/h.