Question 1046994
Two ways to do this at least.
He is 55 miles ahead of you and you are gaining at 10 mph (65-55).  It will take 5.5 hours.
His distance is 55x, where x is the number of hours driven
Your distance is 65(x-1), because you drive for one less hour.
You catch him, so distance is the same and therefore 55x=65(x-1)
distributing
55x=65x-65
-10x=-65, and x=6.5 hours.
but that is not the answer.  The time you have to drive is x-1
so the time is 6.5-1 or 5.5 hours.
In that time, he travels 357.5 miles, multiplying 55 by 6.5
you travel 357.5 miles, multiplying 65*5.5