Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Allen and Brianne to complete the project together. Explain each step.

Question

Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together. 

Write an equation and solve for the time it takes Allen and Brianne to complete the project together. Explain each step.

welshfella · Answer

work out for each person the fraction of the project that they can paint in one hour.
Then the fraction that they can paint together = 1/x  hours  where x is the time taken by them working together.

so in 1 hour Allen paints 1/16 and Brianne paints 1/18
the equation is

1/16  + 1/18  = 1/x

solve for x