Multiple choice

A boat goes $12km$ upstream and $40km$ downstream in $8$hrs. It can go $16km$ downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

  1. Speed of boat in still water $=9km/hr$ and speed of stream $6km/hr$.
  2. Speed of boat in still water $=6km/hr$ and speed of stream $2km/hr$.
  3. Speed of boat in still water $=14km/hr$ and speed of stream $32km/hr$.
  4. Speed of boat in still water $=7km/hr$ and speed of stream $23km/hr$.
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B Correct answer
AI explanation

The boat travels 12 km upstream and 40 km downstream in 8 hours, and it can also travel 16 km downstream in 8 hours. This means the time to travel 40 km downstream equals the time to travel 16 km downstream plus the time to travel 12 km upstream, which implies the boat travels 12 km upstream in the exact same time it travels 24 km downstream. Letting the upstream speed be u and downstream speed be v, we get 12/u = 24/v, so v = 2u; substituting this into the first time equation, 12/u + 40/(2u) = 8, yields an upstream speed of 4 km/hr and a downstream speed of 8 km/hr. The speed of the boat in still water is (8 + 4) / 2 = 6 km/hr, and the speed of the stream is (8 - 4) / 2 = 2 km/hr.

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