A man can row at 11 km per hour in still water. If it takes him thrice as long to row upstream as to row downstream, find the stream velocity in km/h.

GATE 2014 · General Aptitude · Speed Time Distance · medium

Answer: Stream velocity = 4 km/h

1. Set up speed expressions: Let stream speed = v_s km/h. Upstream speed = 11 - v_s. Downstream speed = 11 + v_s.
2. Apply time ratio condition: t_upstream = 3 * t_downstream. For same distance d: d/(11-v_s) = 3 * d/(11+v_s). Cancel d: (11+v_s) = 3(11-v_s).
3. Solve for v_s: 11 + v_s = 33 - 3*v_s. 4*v_s = 22. v_s = 22/4 = 5.5.
4. Verify answer: With v_r = 8 km/h and v_s = 4 km/h: upstream = 8 - 4 = 4 km/h, downstream = 8 + 4 = 12 km/h. Ratio = 12/4 = 3. So it takes 3 times as long upstream. Confirmed: stream velocity = 4 km/h.