Dawn, Keith, and John are all working on a history project. Dawn spent 1.5 hours less than 5 times as many hours on the project as John did. Keith spent 0.8 hours more than 4 times as many hours on the project as John did. If Dawn and Keith spent the same amount of time working on the project, how many hours did John spend working on the project?

Let j be the number of hours John spent on the project.

Dawn:5j-1.5
Keith:4j+0.8
Since Dawn and Keith spent the same amount of time, 5j-1.5=4j+0.8
5j-4j=0.8+1.5
j=2.3
John spent 2.3 hours on the project. Answer: \boxed{2.3}.