Multiple choice

Rekha can row her boat at the speed of $5$ km/hr in still water. If it takes one hour more to row the boat $5.25$ km upstream than to return downstream. Find the speed of the stream.

  1. $9$ km/hr
  2. $5$ km/hr
  3. $2$ km/hr

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of stream be s. Upstream speed = 5-s, downstream speed = 5+s. Time difference: 5.25/(5-s) - 5.25/(5+s) = 1. 5.25 * (5+s - (5-s)) / (25-s^2) = 1. 5.25 * 2s = 25-s^2. 10.5s = 25-s^2. s^2 + 10.5s - 25 = 0. Using quadratic formula: s = (-10.5 + sqrt(110.25 + 100)) / 2 = (-10.5 + 14.5) / 2 = 2.

AI explanation

Let the speed of the stream be x km/hr, making the upstream speed (5 - x) km/hr and the downstream speed (5 + x) km/hr. The time difference for the 5.25 km trip is 1 hour, so 5.25/(5 - x) - 5.25/(5 + x) = 1. Finding a common denominator gives 5.25 times 2x divided by (25 - x^2) equals 1, meaning 10.5x = 25 - x^2. Rearranging gives x^2 + 10.5x - 25 = 0, and solving this quadratic equation yields x = 2. The speed of the stream is 2 km/hr.

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