Use substitution to solve the system.
x = 3y + 8
3x + 5y = 10

So we need to find the length of the hypotenuse of a right triangle with sides of 3 and 4, then add that distance to 3 and 4.

By the Pythagorean Theorme, the hypotenuse squared is equal to the sum of the sides squared...

d^2=3^2+4^2

d^2=9+16

d^2=25

d=√25

d=5

So the total distance of her run is 5+4+3=12 km