Question 5694: This is my second time using this section-the first response was really helpful, so thanks in advance.
My problem is a word problem dealing with fractions with variables.
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?
*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.
Answer by prince_abubu(198)   (Show Source):
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.
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
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.
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.
 <---- This is actually the equation described right above. However, the equivalent equation that you would set up is
 <----- 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.
Simplifying further,  . 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.
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