[tex]v_1=60mph\\
v_2=50mph\\
v_3=55mph\\
t_1- time\ needed\ to\ travel\ from\ X\ to\ Y\ at\ v_1\ and\ return\ with\ v_2\\
t_2- time\ needed\ to\ travel\ from\ X\ to\ Y\ at\ v_3\\\\
t_1-0,5h=t_2\\
s-travelled\ distance\\
v=\frac{s}{t}\\
v*t=s\\
t=\frac{s}{v}\\
\frac{0,5s}{60}+\frac{0,5s}{50}-0,5=\frac{s}{55}\\\\
\frac{1}{120}s+\frac{1}{100}s-\frac{1}{55}s=\frac{1}{2}\\
\frac{1}{6600}s=\frac{1}{2}\\
s=3300miles\\
Distance\ from\ town\ X\ to\ town\ Y\ is 1650miles.
[/tex]
