Question 157522
If they both travel the same route, then meet at some point,
they will have both gone the same distance.
I can write 2 sets of equations with distance, {{{d}}} the same
for both
{{{d = r[1]*t[1]}}}
{{{d = r[2]*t[2]}}}
It is given that {{{r[1] = 45}}}mi/hr
and also given that {{{r[2] = 55}}}mi/hr
Since the 2nd car leaves 1/2 hr later that car 1,
It will have been on the road 1/2 hr less when 
they meet, so {{{t[2] = t[1] - .5}}}
So far I have:
{{{d = 45*t[1]}}}
{{{d = 55*(t[1] - .5)}}}
They both equal {{{d}}}, so I'll set them equal to eachother
{{{45t[1] = 55t[1] - 27.5}}}
{{{10t[1] = 27.5}}}
{{{t[1] = 2.75}}}hrs
This is how long the 1st car is on the road
The 2nd car takes {{{2.75 - .5 = 2.25}}}hrs to catch up
or 2 hrs and 15 min answer