Multiple choice

The ratio of speeds of a motor boat to that of the current of water is $36:5$. The motor boat goes along with the current is $5$ hr $10$ min. Find the time to come back of motor boat ?

  1. $6$ hr, $50$ min
  2. $5$ hr, $40$ min
  3. $7$ hrs
  4. $6$ hr, $30$ min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed of boat be 36k and current be 5k. Downstream speed is 41k, upstream is 31k. Distance = 41k * (310/60) hours. Time taken upstream = Distance / 31k = (41k * 310/60) / 31k = 41 * 310 / (60 * 31) = 41 * 310 / 1860 = 12710 / 1860 = 6.833 hours, which is 6 hours and 50 minutes.

AI explanation

The downstream speed is proportional to 36 + 5 = 41 parts of the ratio. The upstream speed is proportional to 36 - 5 = 31 parts. Since distance is constant, the upstream time is calculated using the inverse ratio as 5 hours 10 minutes multiplied by 41/31, which is 310 minutes times 41/31 to equal 410 minutes. This converts to 6 hours and 50 minutes. The result is 6 hours and 50 minutes.

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