Alex is riding his bicycle to school. after 1 mile, he is a third of the way home. how much farther does he have to go?

Given that cycling 1 mile indicates Alex is 1/3 of the way home, its safe to say that he needs to cycle 2/3 more to reach his destination.

We can look at it this way:
～ 1/3 = 1 mile

～ 2/3 = 1/3 + 1/3
ヽ 2/3 = 1 mile + 1 mile
ヽ 2/3 = 2 miles

～ 3/3 =  1/3 + 1/3 + 1/3
ヽ 3/3 = 1 mile + 1 mile + 1 mile
ヽ 3/3 = 3 miles total to reach home.

3/3 - 1/3 = 2/3
3 miles - 1 mile = 2 miles

As you can see, Alex will need to cycle two more miles in order to complete a full three thirds (3/3) of his journey back home.

Hope this helps! ッ