Last week they had a call where there were 2 ways to get up a hill to a home. One was was steep and the other was gentle but they were both 3.1 miles long. Click and clack said that, since the distance and change in elevation were the same, the fuel consumption would be the same.
I say no. If one route is a consistent slope of a fixed grade and gentle curves it would use the least fuel. If the second route was like a roller coaster with lots of steep ups and downs and many sharp curves, it would use the most fuel. In any case a route that requires the use of the brakes, and the car isn’t a hybrid, will use more fuel since the brakes take kinetic energy and convert it to heat.
There was a lengthy thread on this topic a few days ago, probably scrolled off. A lot of people agreed with you. It had to have ups and downs to be steeper but the same distance. I don’t agree on brakes because not enough info given, thus we have to guess. I can visualize lots of scenarios which comply with basic conditions, but do not require brakes, at least if no cop is watching, heh, heh. But, definitely a lot of extra gas used on each up, since car drive train is not 100% efficient, which means energy gained rolling down is not all available on the next up.
To me, in the end, though tempting, this was a silly question. If we could see the two routes it would be easy to agree. Intelligent people tend to have good imaginations, IMO, and can come up with different logical scenarios when the problem is vague and ambiguous.
Maybe that was the point of the problem. Like the old fairy tale where the young man was in love with the princess. When her dad, the King found out, he ordered the culprit to the stadium. He was forced to choose between two doors, one with a fierce lion; the other with a beautiful woman of his social class whom he was to marry if he chose the door. The culprit looked over at his beloved princess, and she gestured at the left door. So, was she sending him to his death to keep him from the arms of another woman, or did she wish to save his life while losing him? Purely a trick question.
I thought the guy in the two routes problem probably knew he used more gas, but liked all the racing engine noises and squealing tires, sort of Casper Milquetoast imagining he is a NASCAR driver while returning to his house where he mostly cowers and says “Yes, dear.” 