A boat goes 4 km upstream and 4 km downstream in 1 hour. The same boat goes 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of boat in still water?
9
Let \(B\) = boat speed and \(S\) = stream speed. Put \(u=\tfrac{1}{B-S}\), \(d=\tfrac{1}{B+S}\).
Step 1 — Form equations:
\[4u+4d=1,\quad 3u+5d=\tfrac{11}{12}\]
Step 2 — Solve: Multiplying the first by 3 and the second by 4 and subtracting gives \(8d=\tfrac{2}{3}\Rightarrow d=\tfrac{1}{12}\), then \(u=\tfrac{1}{6}\).
Step 3 — Recover speeds: \(B-S=6\), \(B+S=12\), so \(B=9\) km/hr.
Therefore the boat's speed in still water is 9 km/hr.
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