Dawn, Keith, and John are all working on a history project. Dawn spent 1.5 hours less than 6 times as many hours on the project as John did. Keith spent 1.2 hours more than 5 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?

Question

Dawn, Keith, and John are all working on a history project. Dawn spent 1.5 hours less than 6 times as many hours on the project as John did. Keith spent 1.2 hours more than 5 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?

A.
4
B.
There is not enough information.
C.
0.3
D.
2.7

Answer 1

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

Then Dawn spent 6J - 1.5 hours on the project and Keith spent 5J + 1.2 hours on the project.
Since Dawn and Keith spent the same amount of time on the project, 6J - 1.5 = 5J + 1.2.
Subtracting 5J from both sides, J - 1.5 = 1.2.
Adding 1.5 to both sides, J= 2.7. Answer: \boxed{2.7}.