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.

phi · Answer

use the idea that 
rate * time = 1 job

rate is in "jobs per hour"
for example, the rate of Allen is 1/16   (1 job per 16 hours)

you can add up the rates of everybody:
(Allen_rate + Brianne_rate + x) * Time = 1 job
if you know the Time it takes for everybody, you can solve for x, the unknown rate (Charles' rate)

anonymous · Answer

so the equation would be like
1/16 + 1/18 + 1/x = x/x?