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?

Question

A.
0.7
B.
2.3
C.
There is not enough information.
D.
4

Answer 1

Let the number of hours John spent on the project be \( x \).

According to the information provided:

1. Dawn spent 1.5 hours less than 5 times the hours John spent: \[ \text{Dawn's hours} = 5x - 1.5 \]

2. Keith spent 0.8 hours more than 4 times the hours John spent: \[ \text{Keith's hours} = 4x + 0.8 \]

Since Dawn and Keith spent the same amount of time on the project, we can set the equations equal to each other: \[ 5x - 1.5 = 4x + 0.8 \]

Now, we will solve for \( x \):

1. Subtract \( 4x \) from both sides: \[ 5x - 4x - 1.5 = 0.8 \] \[ x - 1.5 = 0.8 \]

2. Add \( 1.5 \) to both sides: \[ x = 0.8 + 1.5 \] \[ x = 2.3 \]

So, John spent \( 2.3 \) hours working on the project.

Thus, the answer is \( \boxed{2.3} \).