Two train start at the same time from two stations and proceed towards each other with speeds $40$ km per hour and $45$ km per hour respectively. When they meet, it is found that one train has travelled $40$ km more than other. Find the distance between the two stations.

Using the relative speed method for trains moving towards each other, their relative speed is the sum of their individual speeds, giving 40 + 45 = 85 km/hr. The difference in their speeds is 45 - 40 = 5 km/hr, meaning the faster train gains 5 km over the slower one each hour. Since the total difference is 40 km, the time taken to meet is 40 divided by 5, which equals 8 hours. The total distance between the stations is their relative speed multiplied by the time, giving 85 multiplied by 8 = 680 km.

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