Multiple choice

A boat sailing up and down a river takes $'m'$ minutes to go one kilometere upstream and $'n'$ minutes to go one kilometre downstream. The speed of the boat relative to the water in the river in kilometre/minute units is

  1. $\dfrac{m + n}{2\, m\, n}$
  2. $\dfrac{m - n}{2\, m\, n}$
  3. $\dfrac{n - m}{2\, m\, n}$
  4. $\dfrac{2(m + n)}{ m\, n}$
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A Correct answer
Explanation

Speed upstream = 1/m km/min. Speed downstream = 1/n km/min. Let boat speed be B and current speed be C. B - C = 1/m and B + C = 1/n. Adding the two equations: 2B = 1/m + 1/n = (n+m)/(mn). So B = (m+n)/(2mn).

AI explanation

Let the upstream and downstream speeds of the boat be (1/m) km/min and (1/n) km/min, respectively. Using the still water speed formula, which is half the sum of the upstream and downstream speeds, we get the boat's speed as (1/2)(1/m + 1/n). Adding these fractions gives a common denominator of mn, resulting in the speed being (m + n) / 2mn km/min. The result is (m + n) / 2mn.

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