<PRE><B>Question 1146053</B>
&lt;br&gt;
The statement of the problem is almost certainly incorrect....&lt;br&gt;
Here is the probable correct statement of the problem, with a solution.&lt;br&gt;
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?&lt;br&gt;
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.&lt;br&gt;
Then the fractions of the job that Mary and Peter do in 1 hour are 1/x and 1/2.5x, respectively.&lt;br&gt;
Together, the fraction of the job they do in 1 hour is 1/12.5:&lt;br&gt;
{{{1/x + 1/2.5x = 1/12.5}}}&lt;br&gt;
Multiply everything by 12.5x to clear fractions:&lt;br&gt;
{{{12.5 + 5 = x}}}
{{{x = 17.5}}}&lt;br&gt;
ANSWER: Mary takes 17.5 hours to do the job alone.&lt;br&gt;
Here is an alternative method for solving the problem which can, in most problems like this, make the work much easier.&lt;br&gt;
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.&lt;br&gt;
With the phrase saying that &quot;Mary works 2.5 times FASTER THAN Peter&quot;, 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.&lt;br&gt;
So the correct setup for the problem AS STATED is&lt;br&gt;
x = number of hours Mary takes alone
3.5x = number of hours Peter takes alone&lt;br&gt;
With that setup, the answer is going to be ugly, so I will use the alternative method for finding the answer.&lt;br&gt;
The ratio of amounts of work done by the two of them is x:3.5x = 1:3.5 = 2:7&lt;br&gt;
The fraction of the job Mary does when the two work together is 7/9.&lt;br&gt;
The number of hours Mary takes to do the job alone is (9/7)*12.5 = (9/7)(25/2) = 225/14.&lt;br&gt;
Since that is an &quot;ugly&quot; answer, it is almost certain that the statement of the problem is incorrect....
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