There was a motor-boat race between two persons. One of them covered a distance of 8 km upstream and 12 km downstream in 6 hr and his competitor covered 10 km upstream and 21 km downstream in 9 hrs in the same boat later on. What is the ratio of the speed of the boat in still water to the speed of the flow of water in the stream?

Let the speed of the boat be B and the speed of the stream be S. The two equations are 8/(B-S) + 12/(B+S) = 6 and 10/(B-S) + 21/(B+S) = 9. Let u = 1/(B-S) and v = 1/(B+S), giving 8u + 12v = 6 and 10u + 21v = 9. Solving these simultaneous equations yields u = 1/2 and v = 1/3, which means B-S = 2 and B+S = 3. Solving for B and S gives the boat speed as 2.5 km/hr and the stream speed as 0.5 km/hr, making the ratio 5:1.

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