Question 1058289
{{{x}}}= distance walked by Mario, in miles
{{{x+1}}}= distance walked by Evan
{{{x+2}}}= distance between Mario and Evan at the end of their walks.
The 3 distances above are the lengths of the sides of a triangle.
Since Mario and Evan walked in directions perpendicular to each other,
their walks are the legs of a right trisngle,
and the  final distance between them is the hypotenuse of that triangle.
According to the Pythagorean theorem,
{{{x^2+(x+1)^2=(x+2)^2}}}
{{{x^2+x^2+2x+1=x^2+4x+4}}}
{{{2x^2+2x+1=x^2+4x+4}}}
{{{x^2-2x-3=0}}}
{{{(x-3)(x+1)=0}}}
{{{x=3}}} is the only positive solution,
so Mario walked {{{highlight(3 miles)}}} ,
and {{{x+1=highlight(4)}}} is the number of miles walked by Evan.
 
NOTE:
The triangle is a 3-4-5 triangle,
the most popular right triangle with whole number side lengths,
and the only one with where the long leg and hypotenuse
are longer than the short leg by 1 and 2 units respectively
(as proven above).
Knowing that, no calvulation is needed,
which would be helpful if this was a multiple choice question.