Multiple choice

The speed of a boat in still water is $15$ km/hr. It can go $30$ km upstream and return downstream to the original point in $4$ hrs $30$ min. The speed of the stream is:

  1. $5$ km / hr
  2. $8$ km/ hr
  3. $10$ km/hr
  4. $15$ km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let stream speed be s. Time = 30/(15-s) + 30/(15+s) = 4.5. 30(15+s+15-s)/(225-s^2) = 4.5. 900/4.5 = 225-s^2. 200 = 225-s^2. s^2 = 25, s = 5.

AI explanation

Let the speed of the stream be x km/hr, making the upstream speed (15 - x) km/hr and the downstream speed (15 + x) km/hr. The total time for the 30 km round trip is 30/(15 - x) + 30/(15 + x), which equals 4 hours 30 minutes or 4.5 hours. Finding a common denominator gives 30 times 30 divided by (225 - x^2) equals 4.5, meaning 225 - x^2 equals 200. Solving for x gives x^2 = 25, so the speed of the stream is 5 km/hr.

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