Question

Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together.

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

Answer 1

I know that we utilize fractions 1/8 and 1/6 (park per hour).

By multiplying to a common denominator, we know that together Cody and Kaitlyn complete 7 jobs per 24 hours.

Answer 2

How do I write this as an equation??

Answer 3

7/24 is the fraction of the project that can be completed by Cody and Kaitlyn working together. The time in hours for the project to be completed by both working is the reciprocal of 7/24. Therefore the required equation for the time t hours needed to complete the project with both working is:
\[\large t=\frac{1}{\frac{1}{6}+\frac{1}{8}}\]