SOLUTION: Leo fnished 2/3 of a job in 12 hours. When he was joined by Ed, they completed the job in 2 hours. How many hours would it take Ed to do the job alone.
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Question 73418This question is from textbook
: Leo fnished 2/3 of a job in 12 hours. When he was joined by Ed, they completed the job in 2 hours. How many hours would it take Ed to do the job alone. This question is from textbook
You can put this solution on YOUR website! Leo fnished 2/3 of a job in 12 hours. When he was joined by Ed, they completed the job in 2 hours. How many hours would it take Ed to do the job alone.
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Leo DATA:
Time = (2/3) job/12 hr = 3/2[(2/3)job/12 hr](2/3)= 2job/36hr=1job/18hr
Rate = (1/18)job/hr.
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Together DATA:
Time = 12 hrs/job ; Rate = (1/12)job/hr
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Ed Data:
Time = x hrs/job ; Rate = (1/x) job/hr
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EQUATION:
rate + rate = rate together
1/18 +1/x = 1/12
Multiply thru by 36x to get:
2x + 36 = 3x
x=36 hrs (Time for Ed to do the job alone.)
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Cheers,
Stan H.
You can put this solution on YOUR website! Leo finished 2/3 of a job in 12 hours; therefore to finish one whole job it would take him 3/2 * 2/3 jobs = 3/2 * 12 hours--- or 18 hours to finish one job. So his rate is 1/18 jobs per hour. When he is joined by Ed it takes them 2 hours
times (1/18 + 1/x) rates to complete the remaining 1/3 of the job left. Thus our equation is 2/18 + 2/x = 1/3. Multiplying by the least common denominator, which is 18x we get:
18x(2/18 + 2/x) = (1/3) 18x
2x + 36 = 6x
36 = 4x
9 = x
So it would take Ed 9 hours working alone to complete the job. Checking:
2/18 + 2/9 = 2/18 + 4/18 = 6/18 = 1/3.
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