Question $2[16$ points$]$

A person drives a large diesel$-$fueled truck from Riyadh to Jeddah at an average speed of $110k\frac{m}{h}.$ The distance he traveled is $990km.$ During this trip, the power consumption is given by the following equation:

$P=P_{\text{a}\text{c}\text{c}}+P_{\text{t}\text{i}\text{r}\text{e}}+P_{\text{a}\text{e}\text{r}\text{o}}$

Where, $P_{\text{a}\text{c}\text{c}}=20(kW)$

$P_{\text{t}\text{i}\text{r}\text{e}}=c_{\text{t}\text{i}\text{r}\text{e}}V,$ where is in $k\frac{m}{h},$ and the result is in $kW$

$P_{\text{a}\text{e}\text{r}\text{o}}=c_{\text{a}\text{c}\text{r}\text{o}}{V}^3,$ where is in $k\frac{m}{h},$ and the result is in $kW$

To reduce diesel consumption on his way back from Jeddah to Riyadh, the driver decides to do the following:

Properly inflate the tires to reduce $c_{\text{t}\text{i}\text{r}\text{e}}$ by $20\%$

Install aerodynamic additives to reduce $c_{\text{a}\text{e}\text{r}\text{o}}$ by $15\%$

Drive at $90k\frac{m}{h}$

The power consumed by the accessories $(P_{\text{a}\text{c}\text{c}})$ remains the same during the return trip.

The efficiency of the diesel engine is $30\%($defined as: power output $/$ rate of heat input from diesel$),$ and the price of diesel is SR $0\mathrm{.}75/$liter$.$ The heating value of a liter of diesel is $36MJ.$

a$.$ How many liters of diesel does the driver consume on the first trip $($from Riyadh to Jeddah$)?[5$ points$]$

b$.$ How many liters of diesel does the driver consume on the second trip $($from Jeddah to Riyadh$)?[6$ points$]$

c$.$ Calculate the savings $($in Saudi Riyals$)$ the driver made in fuel cost in the second trip. $[5$ points$]$