Multiple choice

A steamer going downstream in a river, covers the distance between $2$ towns in $15$ hours. Coming back upstream, it covers this distance in $20$ hours. The speed of the water is $3$ km/hr. Find the distance between two towns.

  1. $360$ km
  2. $220$ km
  3. $180$ km
  4. $120$ km
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A Correct answer
Explanation

Let d be distance and v be boat speed. Downstream: d/(v+3) = 15. Upstream: d/(v-3) = 20. So 15(v+3) = 20(v-3). 15v + 45 = 20v - 60. 5v = 105, v = 21. Distance d = 15(21+3) = 15 * 24 = 360 km.

AI explanation

Let the speed of the steamer in still water be x km/hr. Since distance is speed multiplied by time, the downstream distance is 15 multiplied by (x plus 3) and the upstream distance is 20 multiplied by (x minus 3). Setting them equal gives 15x plus 45 equals 20x minus 60, so 5x equals 105 and x equals 21 km/hr. The distance between the towns is the downstream speed multiplied by the time, which is (21 plus 3) multiplied by 15, equalling 360 km.

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