There was 90 runners to start a race. in the first half of the race, 1/5 of them dropped out. in the second half of the race, 1/3 of the remaining runners dropped out. how many runners finished the race?

48 runners finished the race

Step-by-step explanation:

1/5 of the original 90 runners dropped out during the first half of the race.  To determine how many runners stayed in the race, we subtract 1/5 from 1, obtaining 4/5, and then multiply 90 runners by 4/5:  (4/5)(90 runners) = 72 runners still in the race after the first half of the race.

In the second half, 1/3 of these 72 runners dropped out:  (1/3)(72 runners), or 24.  So (2/3)(72 runners), or 48 runners, finished the race.