Joselyn is a manager at a sign painting company. She has three painters, Allen, Brianne, and Charles. Allen can complete a large project in 16 hours. Brianne can complete the same sized project in 18 hours. Charles is new, so no one knows how long it will take him.

Joselyn assigns them all a large project to complete together. Explain to Joselyn how this project can tell her how long it would take Charles if he worked by himself. Use complete sentences.

Given:

Allen - 1 project in 16 hours - 1/16

Brianne - 1 project in 18 hours - 1/18

Charles - 1 project in x hours - 1/x

I am assuming that the project needs to be done w/in 24 hours.

1/16 + 1/18 + 1/x = 1/24

Common denominator: 16 * 18 * x = 288x

(18x + 16x + 288) / 288x = 1

34x + 288 = 288x

288 = 288x - 34x

288 = 254x

x = 288/254

x = 1.13

Charles is still new, so I think it would take him longer to finish than the other two. x = 1.13 would represent 27 hours.

1.13 x 24 = 27.12 hours.