Hello, been lurking for a while. You all seem like a crowd that might appreciate a brain-teaser.
Two skiers, Jim and Dan are riding up an old, slow chair lift. Jim says to Dan, "Man, I wish they'd upgrade this lift to a high speed lift".
Dan says "no way, I wouldn't want for this part of the mountain to get tracked out faster after a big storm."
Jim replies "Don't worry! If you sit at the top of the lift, you'll notice that a chair arrives every 10 seconds, and 4 skiers get off. But go over to the other side of the mountain where they have the new, high speed lift, ride up that, and sit at the top. You'll see that a chair arrives every 10 seconds and 4 skiers get off there as well. So even though the chairs move faster, you have the same number of chairs per minute, thus the same number of skiers per minute, thus the mountain won't get tracked out faster."
Dan thinks for a minute, and replies, "Jim, you're wrong. If I ride a low speed lift, it takes me 10 minutes to ride to the top, and 10 minutes to ski back down. But if I ride a high speed lift, it takes me 5 minutes to ride to the top, and 10 minutes to ski back down. That means that on a low speed lift, I can do 3 runs per hour, but on a high speed lift, I can do 4 runs per hour. But if I can do 4 runs per hour, than so can everybody else. And if everybody does 4 runs per hour instead of 3, the mountain gets tracked out faster. So you see, your reasoning is faulty!"
Who is right? Jim or Dan? Who's reasoning is faulty, and why? You may assume that in both the high and low speed scenario, there is some constant number of riders at the mountain (say 200) and the resort has only one lift, the one being discussed here, and that every chair on the lift is always full in both scenarios.