Multiple choice

A boat moves along the flow of of river between two fixed points P and Q. It takes 40 minutes when going downstream and takes 120 minutes when going upstream between these two points. What time it will take in still water to cover the distance equal to PQ?

  1. 50 minute

  2. 100 minute

  3. 60 minute

  4. 90 minute
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be boat speed and u be stream speed. Downstream: v + u = D/40. Upstream: v - u = D/120. Adding these: 2v = D/40 + D/120 = 3D/120 + D/120 = 4D/120 = D/30. Thus, v = D/60. The time taken in still water is D/v = 60 minutes.

AI explanation

Let distance be D, boat speed be B, and stream speed be S. The downstream and upstream speeds are B+S and B-S, leading to the time equations D/(B+S) = 40 and D/(B-S) = 120. Expressing D as 40(B+S) and 120(B-S) allows simplification to 3(B-S) = B+S, yielding B = 2S. Substituting B = 2S into D = 40(B+S) gives D = 120S, so the time in still water is D/B = 120S / 2S = 60 minutes.

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