Select the correct answerIf a man walks at the rate of 5 km/hour, he misses a train by 7 minutes. However, if he walks at the rate of 6 km/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is?Options6 km6.26 km4 km7 km

To solve this problem, we need to understand that the difference in time when the man misses the train and when he reaches before the train is 7 minutes (late) + 5 minutes (early) = 12 minutes = 12/60 hours = 0.2 hours.

This time difference is the result of the change in speed from 5 km/hour to 6 km/hour. So, we can set up the equation:

Distance = Speed * Time

Let's denote the distance as D. We can set up the following equation according to the problem:

D/5 - D/6 = 0.2

To solve for D, we first get rid of the fractions by multiplying the whole equation by 30 (which is the least common multiple of 5 and 6):

6D - 5D = 0.2 * 30

This simplifies to:

D = 0.2 * 30 = 6

So, the man covers a distance of 6 km to reach the station. Therefore, the correct answer is 6 km.

To solve this problem, we need to understand that the difference in time when the man misses the train and when he reaches before the train is 7 minutes (late) + 5 minutes (early) = 12 minutes = 1/5 hours.

Let's denote the distance to the station as D (in km).

We know that time = distance / speed.

So, we can set up the following equation using the speeds given and the time difference:

D/5 - D/6 = 1/5

To solve for D, we first get rid of the fractions by multiplying the whole equation by 30 (which is the least common multiple of 5 and 6):

6D - 5D = 6

This simplifies to:

D = 6

So, the man needs to cover a distance of 6 km to reach the station. Therefore, the correct answer is 6 km.