Question 530738: It takes Maria twice as long to complete a certain type of research project as it takes Jude to do the same project. They both worked on a similar type of project and they finished in 1 hour. How long would each of them take to finish this project working alone?
I tried to set it up many ways, like 2x+1x=60 mins but that did not work, then I tried 2/3 + 1/3= 60 but that still came out wrong. I know the correct answer is: Maria 1.5 hours, Jude 3 hours, but I have no idea how to get the equation. Could you please help?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Work problems are fraction problems in disguise.
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I assume they worked on the task together to finish it in 1 hr.
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M does 1/M of the job per hr.
J does 1/J of the job per hr.
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(1/M + 1/J) * x hr = 1 whole job completed
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We are told x = 1 hr, so that's done.
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We are told M's rate of work is 1/2 of J's
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J's rate of work is 1/J
1/2 * 1/J = 1/2J
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substitute 1/2J for 1/M
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(1/2J + 1/J) * 1 hr = 1 whole job completed
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solve
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(J + 2J)/ 2J^2 = 1
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3J /2J^2 = 1
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3J = 2J^2
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2J^2 -3J = 0
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J(2J-3) = 0
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J = 0 or 2J = 3
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However, if J could do the work in 0 hours, then his rate of work would be undefined.
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Therefore, we select 2J = 3, which means J = 3/2.
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J can do the whole job in 3/2 hr working alone.
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M can do the whole job in 2*3/2 = 3 hr working alone.
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We can check this solution to be sure it is correct.
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In 1 hr, J can do 2/3 of the job.
In 1 hr, M can do 1/3 of the job
2/3+1/3 = 1.
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We also can substitute in the original equation as double check.
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(1/3 + 1/(3/2))*1 = 1 ??
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(1/3 + 2/3) = 1
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Correct.
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Answer: J could finish the job in 3/2 hr = 90 min. M could finish the job in 3 hr.
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Done.
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