Multiple choice

A motor boat whose speed is $15$ km/hr in still water goes $30$ km downstream and comes back in $4$ hours $30$ minutes. Determine the speed of the stream.

  1. $12$ km/hr
  2. $9$ km/hr
  3. $5$ km/hr
  4. $3$ km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the stream speed be x. The downstream speed is 15+x and upstream is 15-x. The total time is 30/(15+x) + 30/(15-x) = 4.5. Solving this quadratic equation 30(15-x + 15+x) / (225-x^2) = 4.5 leads to 900 / (225-x^2) = 4.5, so 225-x^2 = 200, x^2 = 25, x = 5.

AI explanation

Let the stream speed be x km/hr, making the downstream speed (15 + x) km/hr and the upstream speed (15 - x) km/hr. The total time for the 30 km trip each way is 4.5 hours, so 30/(15 + x) + 30/(15 - x) = 4.5. Combining the fractions gives 900 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.

Keep practicing — related questions