SOLUTION: My word problem involves the application of rational expressions. Here it is: Dennis can do a job in 4 days. When he and Sue work together, the job takes 2 1/3 days. How long

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Question 1159253: My word problem involves the application of rational expressions. Here it is:
Dennis can do a job in 4 days. When he and Sue work together, the job takes 2 1/3 days. How long would the job take Sue working alone?
These are some of the equations I have used: 1/4+1/x=2 1/3 and 2 1/3 -1/4=1/x.

Thank you.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let's look at the first equation you show that you tried to use. We'll discuss it so you can see how to correct it; then you will be able to work the problem.

1/4 + 1/x = 2 1/3 (or 1/4 + 1/x = 7/3)

The "1/4" is the fraction of the job Dennis does in 1 day, because it takes him 4 days to do the job alone.

Using x as the number of days it takes Sue to do the job alone, "1/x" is the fraction of the job she can do in 1 day.

So the left side of your equation is the fraction of the job Dennis does in 1 day, plus the fraction Sue does in 1 day. Logically, then, the right side should be the fraction of the job they do together in 1 day.

But the right side of your equation is not that fraction -- it is the number of days it takes them to do the job together.

It's easy when you are first learning how to solve problems like this to try to write equations using examples you have seen, without thinking about the meaning of the expressions you are using in the equation. The equation you show says
"fraction Dennis does in one day, plus fraction Sue does in one day, equals total number of days"
If you realize that is what the equation says, you know it makes no sense; the equation has to say that the sum of the two fractions Dennis and Sue do in one day has to equal the FRACTION of the job they do together in one day.

The short message of the preceding paragraph is that you always need to understand exactly what the expressions in the equation mean to make the equation make sense.

So fix your equation to say 1%2F4%2B1%2Fx+=+1%2F%287%2F3%29 instead of 1%2F4%2B1%2Fx+=+7%2F3

Then you will be able to solve the equation and get a reasonable answer.

----------------------------------------------------------

1%2F4%2B1%2Fx+=+1%2F%287%2F3%29
1%2F4%2B1%2Fx+=+3%2F7
1%2Fx+=+3%2F7-1%2F4
1%2Fx+=+12%2F28-7%2F28
1%2Fx+=+5%2F28
x+=+28%2F5

It would take Sue working alone 28/5 hours, or 5 3/5 hours, or 5 hours 36 minutes, to do the job.