The algebraic equation used to answer this question is:
3d + 4(1/2d) = 56.5
This is because he ran d, the distance, three times that week. For the rest of the four days, he ran 1/2 the distance, or half d.
To find the answer, you first distribute:
3d + 2d = 56.5
Add like terms:
5d = 56.5
Divide both side by 5:
5d/5 = 56.5/5
d = 11.3
On the first three days, Luke jogged 11.3 miles. On the remaining days, where he jogged 1/2d, Luke jogged 5.65 miles.
Hope this helps!
