Question

Victoria is a manager at a makeup company. She has two makeup artists, Taylor and Lauren. Taylor can complete a large project in 6 hours. Brianne can complete the project in 8 hours. Victoria wants to know how long it will take them to complete the project together. Write an equation and solve for the time it takes Taylor and Lauren to complete the project together. Explain each step.

Answer 1

The rate of how many projects Taylor can complete can be modeled at x/6 and Brianne can be modelled as x/8. So, by combining the functions and setting equal to 1, you can solve. 

x/6 + x/8 = 1

You have to give common demoninators

4x/24 + 3x/24 = 1

Then add together and cross multiply. Giving you an answer of 24/7 or roughly 3.43 hours when rounded to the nearest hundredth.