Problem $3-$ Passenger train diesel consumption $(35$ pts $)$

There is a train matching the dimension of the Bombardier Bi$-$Level Car traveling from Winnepeg to El Paso, a total distance of $1686$ miles $(2713$ km $).$ The train has a drag coefficient of $1\mathrm{.}8.$ Due to the general nature of train travel, it will cover $\backslash (20\backslash \%\backslash )$ of this distance at $\backslash (24\backslash$mathrm$\{$kph$\},10\backslash \%\backslash )$ of the distance at $50$ kph $,$ and $\backslash (70\backslash \%\backslash )$ of the distance at $95$ kph $.$ The train will spend a total of $15$ hr during this trip waiting at stops.

The train runs on diesel which has an energy density of $\backslash (43\backslash$mathrm$\{$MJ$\}/\backslash$mathrm$\{$kg$\}\backslash ),$ and a mass density of $\backslash (849\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ The train burns the fuel at $\backslash (80\backslash \%\backslash )$ efficiency. The average temperature and pressure of the air over the journey will be approximately $1$ atm and $\backslash (23^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($a$)$ How much time will it take the train to make this joumey? $($travel$,$ days, $5$ pts $)$

$($b$)$ What will the drag force be on this train at each of these three speeds? $($Fd$\mathrm{.}24$khh$,$ Fd$.50$ kph$,$ Fd$.\backslash (95\backslash$mathrm$\{$skph$\},\backslash$mathrm$\{$KN$\},15\backslash$mathrm$\{$pts$\}\backslash ))$

$($c$)$ What will be the total energy expended to fight drag force on this journey? $($Eravel$,$ MJ$,10$ pts$)$

$($d$)$ How much diesel fuel volume will the train spend on the joumey to fight drag $($Vravel$,$ L$,5$ pts$)$