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### Grade 8 - Mathematics9.38 Word Problems - Work It

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?
 Total time in hours Fractional part of the job done in 1 hour Wilma 6 1/6 Greg 10 1/10 Together x 1/x

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.
 Q 1: If six men can do a job in fourteen days, how many would it take to do the job in twenty-one days?4 guys3 guys5 guys Q 2: Bill takes 2 hours to wash 500 dishes and Frank takes 3 hours to wash 450 dishes. How long will they take, working together, to wash 1000 dishes?three and half hourstwo and half hoursone and half hours Q 3: Molly can complete a work in 100 minutes. Sally can complete the same task in two hours. They work together for 30 minutes when Leslie joins and starts helping. They finish the task 20 minutes later. How long would it take Leslie to complete the task alone?3 hours5 hours4 hours Q 4: Sally can paint her room in four hours. Jill can paint the same room in eight hours. How long does it take for both Sally and Jill to paint the room if they are working together?3 1/2 hours4 1/2 hours2 2/3 hours Q 5: A painter can paint the house in 12 hours and the second painter takes 8 hours. How long would it take the two painters to paint the house together?4 1/2 hours5 1/2 hours4 4/5 hours Q 6: Two guys are working on your car. One can complete the job in six hours, but the new guy takes eight hours. They worked together for 2 hours, but the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?3 hours and 20 minutes4 hours and 5 minutes3 hours and 30 minutes Q 7: If takes Fred 5 hours to paint a room by himself. It takes Harry 4 hours to paint the same room by himself. If they work together, how long will it take them to paint the room together?2 2/9 hours2 1/9 hours3 2/9 hours Q 8: Bob and Tim painted a fence in 8 hours working together. Last year, Tim painted the fence by himself. A year before Bob painted the fence by himself and it took 12 hours less than Tim took. How long did Bob and Tim take, when each was painting alone?Bob takes 10 hours and Tim takes 24 hoursBob takes 15 hours and Tim takes 25 hoursBob takes 12 hours and Tim takes 24 hours Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!