John traveled a distance of 8 miles during which he was either running

Two ways.

First, Plugging In The Answers (PITA).
The distance walked can't be 3x the total distance. E is out.
Let's try B or C.
B looks easier to work with. Run half and walk half. Run 4 miles takes 40 minutes. Walk 4 miles takes 2 hours. Total is 2 hours 40 minutes. That's too short. B is out.
We need it to take longer. A is out.
Between C and D, D is easier to work with. Run 3 miles takes 30 minutes. Walk 5 miles takes 2.5 hours. Total is 3 hours. Yay!
Answer choice D.

Second, algebra.
R+W=8 ... ---> ... R=8-W
R/6 + W/2 = 3 ... ---> ... R+3W=18
8-W+3W=18
2W=10
W=5
W/total = 5/8
Answer choice D.


ThatDudeKnowsPITA

Let t denote the number of hours John walked. Then, since the total time is 3 hours, he ran for 3 - t hours. Since John walked at 2 miles per hour for t hours, he walked 2t miles. Since he ran at 6 miles per hour for 3 - t hours, he ran 6(3 - t) miles. Thus, the total distance he covered is 2t + 6(3 - t) miles. We are told that he traveled a total of 8 miles, so let's set the expression we obtained equal to 8:

\(\Rightarrow\) 2t + 6(3 - t) = 8

\(\Rightarrow\) 2t + 18 - 6t = 8

\(\Rightarrow\) -4t = -10

\(\Rightarrow\) t = -10/-4 = 5/2

Thus, John walked for 2t = 2 * 5/2 = 5 miles. It follows that the ratio of the distance he walked to the distance he traveled is 5/8.

Answer: D