
Example: Method 1: It takes Harry 5 hours to clean his room by himself. It only takes his mother 2 hours to clean the entire room by himself. How long will it take if Harry and his mother clean his room together? Solution: It takes Harry 5 hours to clean his room alone, so he does 1/5 of the job each hour. His mother can do the whole job in 2 hours, she does 1/2 of the job each hour. To find how much of the job they do together each hour = 1/5 + 1/2 = 2/10 + 5/10 = 7/10 Working together, Harry and his mom can do 7/10 of the job each hour. For the job to be done, the total amount of work must equal 1. Let x be the number of hours it takes to complete the job, you can multiply this by the rate 7/10, set this equal to 1, Therefore (7/10)x = 1 x = 10/7 = 1 3/7 It takes 1 hour and 3/7 hours for them to clean the room together Example: Method 2: It take Wilma 6 hours to complete a job by herself, and it takes Greg 10 hours to complete the same job by himself. If they work together, how long will it take them to complete the job?
Start off with the unknown. So, let them complete in x hours. In 1 hour they both will completed 1/x hours. We know that Wilma takes 6 hours to complete a job so the job she completes in 1 hour is 1/6 and Greg completes in 1 hour 1/10 of the job In 1 hour both can complete in 1/6 + 1/10 = 8/30 Therefore 1/x = 8/30 x = 30/8 x = 3 6/8 x = 3 3/4 hours Directions: Solve the following problems and show your work. Also write at least 5 examples of your own. 