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 for solutions.
I 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