Question

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

Answer 1

John spent 2.4 hours working on the project.

Step-by-step explanation:

Let,

Number of hours worked by Dawn = x

Number of hours worked by Keith = y

Number of hours worked by John = z

According to given statement;

Dawn spent 1.2 hours less than 6 times as many hours on the project as John did.

x = 6z-1.2     Eqn 1

y = 5z+1.2    Eqn 2

As Dawn and Keith worked same amount, therefore,

Eqn 1 = Eqn 2

$6z-1.2=5z+1.2\\6z-5z=1.2+1.2\\z=2.4$

John spent 2.4 hours working on the project.

Keywords: linear equations, addition

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