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Question 1146053: Mary works 2.5 times faster than Peter. Together, they do a job in 12.5 hours. How long does it take Mary working alone to do the same job?
Found 4 solutions by josgarithmetic, MathTherapy, richwmiller, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Mary works 2.5 times faster than Peter. Together, they do a job in 12.5 hours. How long does it take Mary working alone to do the same job?
If she can do the entire job, alone in 5 hours, how can it possibly take BOTH parties 12.5 hours to do the job?
Obviously, Peter must have slowed them down!
Answer by richwmiller(17219)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The statement of the problem is almost certainly incorrect....
Here is the probable correct statement of the problem, with a solution.
Mary works 2.5 times AS FAST AS Peter. Together, they do a job in 12.5 hours. How long does it take Mary working alone to do the same job?
Let x be the number of hours Mary takes to do the job alone; then 2.5x is the number of hours Peter takes alone.
Then the fractions of the job that Mary and Peter do in 1 hour are 1/x and 1/2.5x, respectively.
Together, the fraction of the job they do in 1 hour is 1/12.5:
Multiply everything by 12.5x to clear fractions:
ANSWER: Mary takes 17.5 hours to do the job alone.
Here is an alternative method for solving the problem which can, in most problems like this, make the work much easier.
The ratio of their rates of work is 1:2.5, or 2:5.
That means when working together Mary does 5/7 of the work and Peter does 2/7.
Then in the 12.5 hours it takes them together to do the job, Mary does 5/7 of the job.
So the number of hours Mary would take to do the job alone is (7/5)*12.5 = 17.5.
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As stated at the beginning of my response, that is PROBABLY the intended answer to the problem. However, with the problem stated as it is, the answer is different.
With the phrase saying that "Mary works 2.5 times FASTER THAN Peter", the grammatically and mathematically correct interpretation is that if Mary takes x hours to do the job alone then the number of hours Peter takes alone is x PLUS 2.5 MORE times x, or 3.5x.
So the correct setup for the problem AS STATED is
x = number of hours Mary takes alone
3.5x = number of hours Peter takes alone
With that setup, the answer is going to be ugly, so I will use the alternative method for finding the answer.
The ratio of amounts of work done by the two of them is x:3.5x = 1:3.5 = 2:7
The fraction of the job Mary does when the two work together is 7/9.
The number of hours Mary takes to do the job alone is (9/7)*12.5 = (9/7)(25/2) = 225/14.
Since that is an "ugly" answer, it is almost certain that the statement of the problem is incorrect....
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