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.

Question

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.

vera_ewing · Answer

@kropot72 Can you please help me?

kropot72 · Answer

Allen can complete 1/16 of a large project in 1 hour.
Brianne can complete 1/18 of a large project in 1 hour.
Let c be the number of hours needed by Charles to complete a large project.
Then Charles can complete 1/c of a large project in 1 hour.
Now we can write the following equation, where n is the number of hours taken to complete a large project when all three are working together:
$$\large n(\frac{1}{16}+\frac{1}{18}+\frac{1}{c})=1\ ............(1)$$
When a large project with all three working is completed and the value of n is known, that value of n can be entered into equation (1) and the equation solved to find the value of c.

kropot72 · Answer

My reply would be clearer if I had written:
"Let c be the number of hours needed by Charles to complete a large project if he worked by himself".

kropot72 · Answer

@vera_ewing Do you follow?