Question

Shawn and Ellie are construction workers. Shawn can complete a concrete job in 4 hours, while Ellie can complete it in 6 hours. The foreman says that it will take them 5 hours to complete it if they work together. Explain each step in solving this equation, and determine if the foreman is correct or not. (10 points)

Answer 1

Shawn can complete a concrete job in 4 hours, in one hour he will do 1/4 of the job.
Ellie can complete a concrete job in 6 hours, in one hour he will do 1/6 of the job.
If Shawn and Ellie work together, they will complete 1/4 + 1/6 of the job in one hour, that is,
Amount of work done by both workers in an hour = 1/4 + 1/6 = 5/12.
 5/12 = 1/x, where x is the number of hours required to complete the job by both men
5/12 = 1/x 
Cross multiply:
5 * x = 12 * 1
5x = 12
x = 12/5 = 2.40
Therefore, if the two men are working together, it will take them 2.40 hours to complete the job.