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Grade 8 - Mathematics9.39 Word Problems on Work

Example:
Method :
• Write or get the algebraic equation.
• Solve for the unknown.
Question: Two people can work a task in 5 hours. If the first person can complete the task alone in 9 hours. How long would it take the second person to complete the same task working alone.
Solution:
 Total time in hours Fractional part of the job done in 1 hour First Person 9 1/9 Second Person x 1/x Together 5 1/5

The first person takes 9 hours to complete the task working alone, implies the person completes 1/9th of the job in each hour.
Let x be the hours it takes second person to complete the task working alone, implies that the person takes 1/x of the job each hour.
Working together it takes the two people to complete the job in 5 hours. That means that each hour 1/5 of the job is getting done.
Therefore 1/9 + 1/x = 1/5
subtracting 1/9 both sides we have
1/9 + 1/x - 1/9= 1/5 - 1/9
1/x = 9/45 - 5/45
1/x = 4/45
x = 45/4 or 11 1/4
The second person takes 11 1/4 hour to finish the working alone.

Directions: Solve the following word problems and show your work. Also write at least 5 word problems of your own.
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