#### jwednesday

##### New member

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I am having trouble setting up word problems like this ...

- Thread starter jwednesday
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I am having trouble setting up word problems like this ...

- Joined
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I already know the answer ... it is 4.8 hours ... I just need the formula to get the answer

Frank does 1/8 of the job in one hour.

Frank and Fred together do 1/3 of the job in one hour.

So 1/8 + 1/x = 1/3, where 1/x is the fraction of the job Fred does in an hour,

therefore x is the number of hours it takes him to do the job.

(x/x)(1/8) + (8/8)(1/x) = 1/3

x/8x + 8/8x = 1/3

(x+8)/8x = 1/3

3(x+8) = 8x

x is the number of hours taken by Fred to do the job.

The thing is to learn these steps.

There will be other ways to.

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The x/x and the 8/8 were not added; they were multiplied. Both the x/x and the 8/8 are equal to 1, as you recognized. Multiplying by one does not change the value of a number -- just the way the number looks.I understand all except for why you added x/x prior to 1/8 and 8/8 prior to 1/x ... I know 8/8 represents "1"

Why would we want to do this? We wanted to combine two fractions into a single expression (a single fraction). To do this, we must first have a common denominator.

Multiplying (x/x)(1/8) = x/(8x).

Multiplying (8/8)(1/x) = 8/(8x).

Now both fractions have the common denominator of "8x", so now they can be combined:

x/(8x) + 8/(8x) = (x + 8)/(8x)

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Apply the same logic discussed in your previous posts - like -jwednesday said:

I am having trouble setting up word problems like this ...

viewtopic.php?f=8&t=37743&p=146446#p146446

Just in case you want to confuse yourself more - read these

http://forums.xkcd.com/viewtopic.php?f=17&t=26912

and

viewtopic.php?f=14&t=35484 (credited to Sir Jonah)

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Fred = 1/x

together = 1/3

1/8 + 1/x = 1/3 .. 3/24 + 1/x = 8/24 .. subtract 3/24 from both sides .. 1/x = 5/24 .. x = 0.208 to solve ... 1/0.208 = 4.8 hours for Fred