![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
\n" ); document.write( "The statement of the problem is almost certainly incorrect....
\n" ); document.write( "Here is the probable correct statement of the problem, with a solution.
\n" ); document.write( "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?
\n" ); document.write( "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.
\n" ); document.write( "Then the fractions of the job that Mary and Peter do in 1 hour are 1/x and 1/2.5x, respectively.
\n" ); document.write( "Together, the fraction of the job they do in 1 hour is 1/12.5:
\n" ); document.write( "
\n" ); document.write( "Multiply everything by 12.5x to clear fractions:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "ANSWER: Mary takes 17.5 hours to do the job alone.
\n" ); document.write( "Here is an alternative method for solving the problem which can, in most problems like this, make the work much easier.
\n" ); document.write( "The ratio of their rates of work is 1:2.5, or 2:5.
\n" ); document.write( "That means when working together Mary does 5/7 of the work and Peter does 2/7.
\n" ); document.write( "Then in the 12.5 hours it takes them together to do the job, Mary does 5/7 of the job.
\n" ); document.write( "So the number of hours Mary would take to do the job alone is (7/5)*12.5 = 17.5.
\n" ); document.write( "------------------------------------------------------
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "So the correct setup for the problem AS STATED is
\n" ); document.write( "x = number of hours Mary takes alone
\n" ); document.write( "3.5x = number of hours Peter takes alone
\n" ); document.write( "With that setup, the answer is going to be ugly, so I will use the alternative method for finding the answer.
\n" ); document.write( "The ratio of amounts of work done by the two of them is x:3.5x = 1:3.5 = 2:7
\n" ); document.write( "The fraction of the job Mary does when the two work together is 7/9.
\n" ); document.write( "The number of hours Mary takes to do the job alone is (9/7)*12.5 = (9/7)(25/2) = 225/14.
\n" ); document.write( "Since that is an \"ugly\" answer, it is almost certain that the statement of the problem is incorrect....
\n" ); document.write( " \n" ); document.write( "