You have {{{R=unknown}}}, something for which to solve;
{{{T=5&1/4}}} hours;
{{{D=350}}} miles.
Keep your calculations in miles per hour.
{{{R=D/T}}}
{{{R=350/(5&1/4)}}} miles per hour
You have no reason to convert anything into minutes. Your given values are in miles and in hours, and a very common unit for travel rates is MILES per HOUR.