$\begin{array}{l}
Let\,the\,car\,turn\,of\,the\,highway\,at\,a\,{\rm{distance }}\\
'x'\,from\,the\,{\rm{point}}\,M.\,So,\,RM = x\\
And\,if\,speed\,of\,car\,in\,field\,is\,v,\,then\,time\,\\
taken\,by\,the\,car\,to\,{\rm{cover}}\,{\rm{the}}\,{\rm{distance}}\,{\rm{QR = }}\\
{\rm{QM}}\, – {\rm{x}}\,{\rm{on}}\,the\,highway,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,{t_1} = \frac{{QM – x}}{{2v}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,…\left( i \right)\\
Time\,taken\,to\,travel\,the\,{\rm{distance}}\,'R\,P'\,in\,the\\
filed\\
\,\,\,\,\,\,\,\,\,\,\,\,\,{t_2} = \frac{{\sqrt {{d^2} + {x^2}} }}{v}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,….\left( {ii} \right)
\end{array}$

$\begin{array}{l}
Total\,time\,elapsed\,to\,move\,the\,car\,form\,Q\\
to\,P\\
t = {t_1} + {t_2} = \frac{{QM – x}}{{2v}} + \frac{{\sqrt {{d^2} + {x^2}} }}{v}\,\,\,\,\,\\
For't'\,to\,be\,mimimum\,\frac{{dt}}{{dx}} = 0\\
\frac{1}{v}\left[ { – \frac{1}{2} + \frac{x}{{\sqrt {{d^2} + {x^2}} }}} \right] = 0\\
\,\,\,\,\,\,\,\,\,\,\,or\,x = \frac{d}{{\sqrt {{2^2} – 1} }} = \frac{d}{{\sqrt 3 }}
\end{array}$