This is another intriguing problem from Presh Talwalkar.

“A car travels 75 miles per hour (mph) downhill, 60 mph on flat roads, and 50 mph uphill. It takes 3 hours to go from town A to B, and it takes 3 hours and 30 minutes for return journey by the same route. What is the distance in miles between towns A and B?”

See the Impossible Car Riddle

Tayeb KazemiI solved the problem assuming there was only downhill and flat on the first leg and flat and uphill on the return. In this case the length of the uphill/downhill can be calculated easily:

assuming this length to be x1, The difference between first leg and return x1/50 -x1/75= 0.5

Therefore x1 = 75m which takes 1hour. meaning the flat length is 120m taking 2hours

Total length = 75+120= 195m