After 3/4 hours, 2/3 of project is done.
After 1 hr, .... project is done.
In other words,
2/3 of project ---- 3/4 hours
? of project ------ 1 hour
The more Katie works, the more the project nears completion. This is a direct proportionality kind of relationship.
Therefore,
Part of project completed in 1 hour = (2/3*1)/(3/4) = 2/3*4/3 = 8/9