Cougar Mountain, a medium$-$sized and profitable ski resort, currently has a traditional fixed$-$grip quad lift 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, Cougar Mountain$$s owner, Jessica Powder, is concerned that the traditional $($a$.$k$.$a$.,$ slow$)$ 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 officer, Doug Bowl, to collect some data on the current lift and the proposed new one. Once he had the data, listed in Table $2\mathrm{.}7,$ he met with Jessica and Mark Ketting, who is responsible for Cougar$$s sales and advertising.

Table $2\mathrm{.}7$

Fixed $-$Grip Detachable

Length of lift $($meters$)700700$

Passengers per chair $44$

Time from bottom to top $($sec$)250125$

Unloading capacity $($skiers per hour$)24002400$

Mark immediately started the conversation by saying, $$Customers are going to love that their ride time will be cut in half by the new lift. But there must be a mistake in Doug$$s 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$$t the unloading capacity double?$$ Doug responded, $$I think the table is correct because from what I have observed, people are not able to load onto a detachable lift any faster than on a fixed$-$grip lift.$$ Jessica jumped in$,$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

$1-$Give an introduction

$2-$Do all the skiers that get on the lift at the bottom get off the lift at the top?

$3-$ What is the difference between the $2$ lifts?

$4-$ What are the implications?

$5-$ Who is correct? Mark $($Unloading capacity should be twice as much$)$ or Doug $($the two lifts have the same capacity$)$

$6-$ How did you use Little$$s Law?

$7-$ Conclusion