Problem source

A single stream of cars, each of width $a$
and exactly in line, is passing along a straight road
of breadth $b$ with speed $V$. The distance between the
successive cars is $c$.
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\end{center}
A chicken crosses the road in safety
at a constant speed $u$ in a straight line  making
an angle $\theta$ with the direction of traffic. 
Show that
\[u\geqslant
\frac{Va}{c\sin\theta+a\cos\theta}.\]
Show also that if the chicken chooses $\theta$ and $u$
so that it crosses the road
at the least possible uniform speed, it crosses
in time
\[\frac{b}{V}\left(\frac{c}{a}+\frac{a}{c}\right)
.
\]