Multiple choice

A boat can travel a distance of 8.5 km in one hour in still water. If the same boat travels upstream for 72 km and then returns to the starting point, taking 17 hours for the entire journey, then what is the speed of the stream?

  1. 0.5 km/hr

  2. 0.25 km/hr

  3. 0.05 km/hr

  4. 0.025 km/hr

  5. 0.005 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be stream speed. Boat speed = 8.5. Upstream speed = 8.5-v, downstream = 8.5+v. 72/(8.5-v) + 72/(8.5+v) = 17. 72 * (8.5+v + 8.5-v) / (8.5^2 - v^2) = 17. 72 * 17 / (72.25 - v^2) = 17. 72 = 72.25 - v^2. v^2 = 0.25, v = 0.5.

AI explanation

Using the upstream and downstream speed formulas, let the speed of the stream be x km/hr, making the upstream speed (8.5 - x) and the downstream speed (8.5 + x). The total time of 17 hours equals the sum of the upstream time and the downstream time, so 72/(8.5 - x) + 72/(8.5 + x) = 17. Multiplying by the common denominator gives 72(8.5 + x) + 72(8.5 - x) = 17(72.25 - x^2), which simplifies to 1224 = 1228.25 - 17x^2. Solving for x^2 gives 4.25 = 17x^2, so x^2 = 0.25. Since x must be positive, the speed of the stream is 0.5 km/hr.

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