Dawn, Keith, and John are all working on a history project. Dawn spent 1.2 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?

Question

A.
0.4
B.
2
C.
4
D.
There is not enough information.

Answer 1

Let's denote the number of hours John spent working on the project as \( J \).

According to the problem:

• Dawn spent \( 5J - 1.2 \) hours.
• Keith spent \( 4J + 0.8 \) hours.

We know that Dawn and Keith spent the same amount of time working on the project, so we can set up the equation:

\[ 5J - 1.2 = 4J + 0.8 \]

Now, let's solve for \( J \).

1. Subtract \( 4J \) from both sides:

\[ 5J - 4J - 1.2 = 0.8 \]

This simplifies to:

\[ J - 1.2 = 0.8 \]

2. Now, add \( 1.2 \) to both sides:

\[ J = 0.8 + 1.2 \]

This gives:

\[ J = 2 \]

Therefore, John spent \( \boxed{2} \) hours working on the project.