Question 700031
{{{t}}} = time in hours since 11:00 AM
10 minutes = {{{10/60=1/6}}} hours
The distance from Old Towne station after {{{t}}} is
{{{30t}}} for the freight train, and
{{{45(t-1/6)=45t-45/6=45t-7.5}}} for the passenger train.
When the passenger train catches up to the freight train,
{{{45t-7.5=30t}}} --> {{{45t-7.5-30t=30t-30y}}} --> {{{15t-7.5=0}}} --> {{{15t-7.5+7.5=0+7.5}}} --> {{{15t=7.5}}} --> {{{15t/15=7.5/15}}} --> {{{highlight(t=0.5)}}}
The passenger train catches up to the freight train 0.5 hours (half an hour, or 30 minutes) after 11:00 AM, at 11:30 AM.