Question 67593
The 1st question I asked myself is, how far have they gone when they meet?
{{{d[1] = 44(t + 1)}}}
{{{d[2] = 48t}}}
At t = 0
{{{d[1] = 44}}
{{{d[2] = 0}}}
At t = 1
{{{d[1] = 88}}
{{{d[2] = 48}}}
At t = 2
{{{d[1] = 132}}}
{{{d[2] = 96}}}
notice they're getting closer together
When they meet {{{d[1] = d[2]}}}
44(t + 1) = 48t}}}
48t - 44t = 44}}}
{{{4t = 44}}}
{{{t = 11}}} 
They meet 11 hours after the 2nd bus leaves, 
12 hours after the 1st bus leaves
{{{d = 44(11 + 1)}}}
{{{d = 528}}} mi
{{{d = 48*11}}}
{{{d = 528}}}mi so, {{{d[1] = d[2]}}}
If they are getting closer together after starting out 44 mi apart,
they can never be 274 mi apart before they meet
Let's call their meeting point the new starting line and a new t = 0.
{{{d[1] = 44t}}}
{{{d[2] = 48t}}}
{{{d[2] - d[1] = 274}}}
{{{48t - 44t = 274}}}
{{{4t = 274}}}
{{{t = 68.5}}}hrs
{{{12 + 68.5 = 80.5}}} = hours since 1st bus left at 1 PM
{{{ 80.5 / 24 }}} = 3 days and 8.5 hours
Add 8.5 to 1 pm to get 9:30 PM 3 days later