Answer
He has traveled 290 miles.
Work Step by Step
$\bf{\text{l. Familiarize yourself with the problem.}}$
The halfway point of the race is at 250 miles.
At this point, the distances from start and finish are equal.
With every x mile over the halfway point,
the distance from the start is $250+x,$
the distance from the finish is $250-x.$
We need $(250-x)$ to be 80 miles less than $(250+x)$
$\bf{\text{2. Translate to mathematical language. (This often means writing an equation.)}}$
$250-x=250+x-80$
$\bf{\text{3. Carry out some mathematical manipulation. (This often means solving an equation.)}}$
... simplify
$ 250-x=170+x\qquad$... add $x-170$ to both sides
$80=2x$
$x=40$
40 miles from the halfway point is 290 miles from the start.
$\bf{\text{4. Check your possible answer in the original problem.}}$
If he travels 290 miles, he has another 210 miles to complete the race.
Is he 80 miles closer to the finish than he is to the start?
Yes.
$\bf{\text{5. State the answer clearly, using a complete sentence.}}$
He has traveled 290 miles.
