It will take 5.25 hours to the second car to overtake the first car, and the first car will have traveled during 8.25 hours.
Why?
To calculate how long before the second car overtakes the first one, we need to make the equations of both cars equal.
For the first car, we have:
[tex]x=x_o + v_{1}*t\\\\x=x_o + v_{1}*(3 hours + t)[/tex]
For the second car, we have:
[tex]x=x_o + v_{2}*t\\\\x=x_o + v_{2}*(t)[/tex]
Making both equations equal, we have:
[tex]35mph*(3hours+t)=55mph*t\\\\105+35t=55t\\\\105=55t-35t\\\\t=5.25[/tex]
Hence, we have that it will take 5.25 hours to the second car to overtake the first car, and the first car will have traveled during 8.25 hours.
Have a nice day!
