If a man walks at the rate of 5km/hr, he misses a train by only 7min. However if he walks at the rate of 6 km/hr he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station?

general knowledge

  1. 5 km

  2. 6 km

  3. 7 km

  4. 8 km

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Correct Option: B

AI Explanation

To solve this problem, let's assume the distance covered by the man to reach the station is "d" kilometers.

We are given two scenarios:

  1. When the man walks at 5 km/hr, he misses the train by 7 minutes.
  2. When the man walks at 6 km/hr, he reaches the station 5 minutes before the arrival of the train.

Let's calculate the time taken in each scenario:

  1. When the man walks at 5 km/hr: Time taken = Distance / Speed = d / 5 km/hr

In this scenario, the man misses the train by 7 minutes, which is equivalent to 7/60 hours. So, the time taken to reach the station is d / 5 km/hr + 7/60 hours.

  1. When the man walks at 6 km/hr: Time taken = Distance / Speed = d / 6 km/hr

In this scenario, the man reaches the station 5 minutes before the arrival of the train, which is equivalent to 5/60 hours. So, the time taken to reach the station is d / 6 km/hr - 5/60 hours.

Now, let's set up the equation using the above information:

d / 5 km/hr + 7/60 hours = d / 6 km/hr - 5/60 hours

To simplify the equation, let's convert all the hours to minutes:

d / (5 * 60) + 7 = d / (6 * 60) - 5

Now, let's solve this equation to find the value of "d":

d / 300 + 7 = d / 360 - 5 d / 300 - d / 360 = -5 - 7 (6d - 5d) / (300 * 360) = -12 d / (300 * 360) = -12 d = -12 * (300 * 360)

Since distance cannot be negative, this equation does not have a valid solution.

Therefore, there is an error in the question or provided information, as it is not possible to solve for the distance covered by the man to reach the station.

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