Frank and Fred Q3

jwednesday

New member
Frank can do in 8 hours a job that he and Fred can do together in 3 hours. How many hours would it take Fred to do the job by himself?

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

chrisr

Full Member
Frank can do 3 jobs in 24 hours.
Frank and Fred together can do 8 jobs in 24 hours.

How many of those jobs were done by Frank?
Therefore how many were done by Fred?

Finally, from that, how long would it take Fred to do one job?

jwednesday

New member
I already know the answer ... it is 4.8 hours ... I just need the formula to get the answer

chrisr

Full Member
Ok,
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.

jwednesday

New member
Ok, 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"

wjm11

Senior Member
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"
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.

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)

Subhotosh Khan

Super Moderator
Staff member
jwednesday said:
Frank can do in 8 hours a job that he and Fred can do together in 3 hours. How many hours would it take Fred to do the job by himself?

I am having trouble setting up word problems like this ...
Apply the same logic discussed in your previous posts - like -

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

Just in case you want to confuse yourself more - read these amusing posts at:

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

and

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

jwednesday

New member
Frank = x/8

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