Karen earns $54.60 for working 6 hours. If the amount she earns varies directly with the number of hours she works, how many hours would she need to work to earn an
additional $260?

Given:

Karen earns $54.60 for working 6 hours.

Amount she earns varies directly with the  number of hours she works.

She need to work to earn an  additional $260.

To find:

Number of hours she need to work to earn an  additional $260.

Solution:

Let the amount of earnings be A and number of hours be t.

According to question,

    ...(i)

where, k is constant of proportionality.

Karen earns $54.60 for working 6 hours.

Divide both sides by 6.

Put k=9.1 in (i).

Substitute A=260 in the above equation.

Divide both sides by 9.1.

Therefore, she need to work extra about 29 hours to earn an  additional $260.