Multiple choice

A motor boat going down stream overcame a raft at a point A, $60$ minute later it turned back and some time passed the raft at a distance of $6km$ from the point A. Assuming the duty of the engine to be constant, the flow of velocity is

  1. $3km{h}^{-1}$
  2. $km{h}^{-1}$
  3. $5km{h}^{-1}$
  4. $6km{h}^{-1}$
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A Correct answer
Explanation

Let v be boat speed and u be stream speed. The raft moves at speed u. The boat travels downstream for 1 hour (60 min), then turns back. The relative speed of the boat and raft is (v+u) - u = v downstream and (v-u) + u = v upstream. The distance covered by the raft in the time the boat returns is 6km. This setup implies the stream velocity is 3km/h.

AI explanation

The raft drifts 6 km from point A in the total time it took the boat to travel downstream, turn around, and travel back upstream to meet it. Because the raft moves at the exact speed of the current, the velocity of the river flow is the total distance the raft drifted divided by the total time of the journey. The total time from meeting the raft initially until passing it again is exactly the 60 minutes the boat traveled downstream plus the time it spent traveling upstream, which is a combined 120 minutes or 2 hours. Therefore, the flow velocity is 6 km divided by 2 hours, which is 3 km per hour. The result is 3km{h}^{-1}.

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