Multiple choice

If a boat takes 4 hours longer to travel a distance of 45 km upstream than to travel the same distance downstream, then find the speed of the boat in still water if the speed of the stream is 2 km/hour.

  1. 7

  2. 14

  3. 10

  4. 9
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A Correct answer
Explanation

Let boat speed be x. Upstream speed = x-2, downstream = x+2. 45/(x-2) - 45/(x+2) = 4. 45(x+2 - x+2) / (x^2-4) = 4 => 45(4) = 4(x^2-4) => 45 = x^2-4 => x^2 = 49 => x = 7.

AI explanation

Using the upstream and downstream speed formulas, we set the time difference to 4 hours: 45 / (v - 2) - 45 / (v + 2) = 4. Finding a common denominator and simplifying yields 180 = 4(v^2 - 4), so v^2 equals 49. Taking the positive square root gives the boat speed in still water as 7 km/hour.

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