Bonus Question (20 Credits) Those of you who are skiers or snowboarders know that some resorts...

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Bonus Question (20 Credits) Those of you who are skiers or snowboarders know that some resorts have "high-speed" chair lifts. These lifts are called "detachable" because the chair detaches from the main cable just before loading people. Once the passengers are "on board," the chair reattaches to the main cable and "rockets" to the top at a much faster speed than the traditional "fixed-grip" counterparts that remain firmly attached to the main cable. Powder Mountain, a medium-sized and profitable ski resort, currently has a traditional fixed- grip quad life that takes guests from the main lodge at the bottom of the mountain up to the peak. While it prides itself on the quality of its terrain and friendly service, Powder Mountain's owner, Jessica Powder, is concerned that the traditional fixed-grip lift will start to deter its established guests from returning year after year. It is time for it to consider replacing the traditional lift with a high-speed quad. Jessica asked her chief operating office, Doug Bowl, to collect some data from Moon Valley, a similar ski resort using the detachable lift. Once he had the data, listed in the Table below, he met with Jessica. Length of lift (meters) Passengers per chair Time from bottom to top (sec) Unloading Passengers (skiers per hour) Powder Mountain (Fixed-Grip) 700 4 250 2400 Moon Valley (Detachable) 700 4 125 2400 Jessica immediately started the conversation by saying, "Customers are going to love that their ride time will be cut in half by the new lift. But there must be a mistake in your data. If the new lift doubles the speed at which skiers travel up the mountain, then it must be that it can unload more skiers at the top at a faster rate. Shouldn't the unloading number double?" Dough was very sure about the data he collected. Then, Jessica got confused, "Doug, assuming you are right, and I am not sure you are, does that mean the only difference between a fixed-grip and a detachable lift is that one moves faster than the other?" Question: If you were Doug, can you explain to Jessica what the problem is? Bonus Question (20 Credits) Those of you who are skiers or snowboarders know that some resorts have "high-speed" chair lifts. These lifts are called "detachable" because the chair detaches from the main cable just before loading people. Once the passengers are "on board," the chair reattaches to the main cable and "rockets" to the top at a much faster speed than the traditional "fixed-grip" counterparts that remain firmly attached to the main cable. Powder Mountain, a medium-sized and profitable ski resort, currently has a traditional fixed- grip quad life that takes guests from the main lodge at the bottom of the mountain up to the peak. While it prides itself on the quality of its terrain and friendly service, Powder Mountain's owner, Jessica Powder, is concerned that the traditional fixed-grip lift will start to deter its established guests from returning year after year. It is time for it to consider replacing the traditional lift with a high-speed quad. Jessica asked her chief operating office, Doug Bowl, to collect some data from Moon Valley, a similar ski resort using the detachable lift. Once he had the data, listed in the Table below, he met with Jessica. Length of lift (meters) Passengers per chair Time from bottom to top (sec) Unloading Passengers (skiers per hour) Powder Mountain (Fixed-Grip) 700 4 250 2400 Moon Valley (Detachable) 700 4 125 2400 Jessica immediately started the conversation by saying, "Customers are going to love that their ride time will be cut in half by the new lift. But there must be a mistake in your data. If the new lift doubles the speed at which skiers travel up the mountain, then it must be that it can unload more skiers at the top at a faster rate. Shouldn't the unloading number double?" Dough was very sure about the data he collected. Then, Jessica got confused, "Doug, assuming you are right, and I am not sure you are, does that mean the only difference between a fixed-grip and a detachable lift is that one moves faster than the other?" Question: If you were Doug, can you explain to Jessica what the problem is?