document.write( "Question 5694: This is my second time using this section-the first response was really helpful, so thanks in advance.
\n" ); document.write( " My problem is a word problem dealing with fractions with variables.\r
\n" ); document.write( "\n" ); document.write( "One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?\r
\n" ); document.write( "\n" ); document.write( "*I set up a table with the first person's work rate at 1/8 multiplied by the time h-2, and the second persons work rate at 1/12 multiplied by the time h. From there, I can't seem find what the problem is looking for. \n" ); document.write( "

Algebra.Com's Answer #2928 by prince_abubu(198) $\"\"$ $\"About$

You can put this solution on YOUR website!
Your thinking and set up make lots of sense. However, there is a tricky thing about work rate problems that your teacher may not point out, especially if one of the workers works some time after his/her co-worker begins the job. One rule is that you NEVER multiply a rate with a time quantity with a minus sign. The second rule is, the variable you're solving for is the actual time it took both people to do the REMAINING part of the job TOGETHER.\r
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\n" ); document.write( "\n" ); document.write( "OK. The first person worked two hours less. So we took h to be the time person 2 did the job, so it makes sense to knock off two hours from person 1's time, thus person 1's time is h - 2, like most of us will think. So then for now, our equation will look like\r
\n" ); document.write( "\n" ); document.write( " $\"+%281%2F8%29%28h-2%29%2B%281%2F12%29h+=+1+\"$ \r
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\n" ); document.write( "\n" ); document.write( "However, that won't give you the right answer. Think about it this way. During the two hours that person 1 didn't work, person 2 was doing his job, right? That means person 2 did 1/6 of the entire job during the two hours that person 1 was just sitting there doing nothing. This would mean that once person 1 joins person 2, there's 5/6 of the job left for both of them to work on.\r
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\n" ); document.write( "\n" ); document.write( "So, the big equation is: the amount done by person 1 in h hours + the amount done by person 2 in h hours + the amount done by person 2 when person 1 wasn't working = the entire job. As mentioned previously, h will automatically be the time it takes for them working together to finish the remaining job.\r
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\n" ); document.write( "\n" ); document.write( " $\"+%281%2F8%29h+%2B+%281%2F12%29h+%2B+%281%2F12%29%2A2+=+1+\"$ <---- This is actually the equation described right above. However, the equivalent equation that you would set up is\r
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\n" ); document.write( "\n" ); document.write( " $\"+%281%2F8%29h+%2B+%281%2F12%29%28h+%2B+2%29+=+1+\"$ <----- In this equation, you're focusing on the fact that person 2 worked 2 hours more than person 1 instead of person 1 working 2 hours less than person 2.\r
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\n" ); document.write( "\n" ); document.write( "Simplifying further, $\"+%285%2F24%29%2Ah+=+5%2F6+\"$ . h = 4 hours. So it took 4 hours to finish the job since person 1 started working 2 hours after person 2 did his portion alone.\r
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