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

Cody ALONE = 8 hours 
Kaitlyn ALONE = 6 hours 
Let Joseph ALONE take j hours 
Cody ALONE in 1 HOUR = 1/8 of the work Kaitlyn ALONE in 1 hour = 1/6 of the work Joseph ALONE in 1 HOUR = 1/j of the work 
Since TOGETHER they take X hours, in 1 hour TOGETHER they complete 1 / X of the work 
1/8 + 1/6 + 1/j = 1/X 
1/j = 1/X - 1/8 - 1/6 = (24 - 3X - 4X ) /24X = (24 - 7X ) / 24X 
j = 24X / ( 24- 7X ) 
After completing the work value of X will be known , calculate j from the above formula ANSWER