Question

Help? :-(

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.

I know that it'll be 1/16 + 1/18 = 1 ? And I know you're supposed to find the common denominator and all that but I'm so confused for some reason. Can someone walk me through this please?

Answer 1

Are you confused on finding the common denominator?

Answer 2

I actually think I solved the problem, but I'm not sure if it's right?

1/16 + 1/18 = 1/1

So, find the common denominator, which is 144.

9/144 + 8/144 = 1/144

18/144 = 8. so together, they can complete it in 8 hours.

Answer 3

9+8=17

Answer 4

It takes them x hours to do the job together.

Allen can complete a large project in 16 hours.
Brianne can complete the project in 18 hours.
Allen and Brianne can complete the project in x hours.

In 1 hour, Allen does 1/16 of the job.
In 1 hour, Brianne does 1/18 of the job.
In 1 hour, Allen & Brianne combined do 1/x of the job.

When they work together for 1 hour, they do

1/16 + 1/18 = 1/x

Solve for x

9/144 + 8/144 = 1/x

17/144 = 1/x

x = 144/17