If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?
It is impossible.
He travelled halfway, which is 30 km. He has to travel another 30 km. In total, he has to travel 60 km with an average speed of 60 km/hour – this means his total travelling time must be 1 hour, but he has already taken 1 hour for his first trip. Unless he is able to teleport himself for the second trip, he will never be able to make it.
Some say that he should travel at 90km/hour for the return trip. Let’s work it out. For the first trip, he travelled at 30km/hour and covered 30km (halfway to the town) in 1 hour. For the second trip, if he travelled at 90km/hour, he would take 20 minutes to cover 30km. His total travelling time will be 1hr and 20 mins (80 mins) and he would have travelled 60km in total. His average speed would be 45 km/hour and not 60 km/hour.