Multiple choice

The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boating till water.

  1. Speed of boat = 8 km/h & Speed of stream $= 3$ km/hr
  2. Speed of boat = 8 km/h & Speed of stream $= 4$ km/hr
  3. Speed of boat = 7 km/h & Speed of stream $= 2$ km/hr

  4. Data insufficient
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A Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 30/u + 44/v = 10 and 40/u + 55/v = 13. Solving this system yields u = 5 km/h and v = 11 km/h. Boat speed = (11+5)/2 = 8 km/h; stream speed = (11-5)/2 = 3 km/h.

AI explanation

Using the distance formula, the first condition yields 30/u + 44/d = 10 and the second yields 40/u + 55/d = 13. Solving this system of equations gives the upstream speed u = 5 km/hr and the downstream speed d = 11 km/hr. The boat speed in still water is (11 + 5)/2 = 8 km/hr, and the stream speed is (11 - 5)/2 = 3 km/hr. The result is a boat speed of 8 km/h and a stream speed of 3 km/hr.

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