Multiple choice

The speed of a boat in still water is $11$ km/hr and the speed of the stream is $x$ km/hr. Find in terms of $x$, the speed of boat upstream and the speed of boat downstream. If the boat takes $\displaystyle 2\frac{3}{4}$ hours to go 12 km upstream and then return, find the value of $x$.

  1. $1$
  2. $5$
  3. $9$
  4. $13$
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B Correct answer
Explanation

Upstream speed = 11-x, downstream = 11+x. Time = 12/(11-x) + 12/(11+x) = 11/4. Solving for x: 12(11+x+11-x)/(121-x^2) = 11/4. 12(22)/(121-x^2) = 11/4. 264/(121-x^2) = 11/4. 24/(121-x^2) = 1/4. 96 = 121-x^2. x^2 = 25, x = 5.

AI explanation

Let the speed of the stream be x km/hr, making the upstream speed (11 - x) km/hr and the downstream speed (11 + x) km/hr. The total time to go 12 km upstream and return is 12/(11 - x) + 12/(11 + x), which equals 2.75 or 11/4 hours. Multiplying by the common denominator yields 12 times 22 divided by (121 - x^2) equals 11/4, so 121 - x^2 equals 96. Solving for x gives x^2 = 25, so the speed of the stream is 5 km/hr.

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