SOLUTION: A clerk can process 350 forms in 2 3/5 days. It takes 1 2/3 days for another clerk to process the same 350 forms. If both clerks work together, how long will it take them to proces

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Question 246035: A clerk can process 350 forms in 2 3/5 days. It takes 1 2/3 days for another clerk to process the same 350 forms. If both clerks work together, how long will it take them to process the 350 forms?
I have tried to work it out and got the following:
Clerk 1 can do 350/(13/5) forms per day = 1750/13 forms per day
Clerk 2 can do 350/(5/3) forms per day = 1050/5 forms per day
I have no idea where to go from there as the bases aren't equal and I'm not sure if I went about it correctly to begin with :| Any help is greatly appreciated!
Answer by marcsam823(57) (Show Source):
You can put this solution on YOUR website!
Let x = the total number of days it will take both clerks to do the job
Convert both mixed numbers to fractions:
Clerk 1 can do the job in 2 3/5 or 13/5 days
Clerk 2 can do the job in 1 2/3 or 5/3 days
This type of problem can be tricky because it requires a bit of a leap in logic. The key to this problem is determining what fraction of the job each clerk can do in one day and adding those two numbers together.

Clerk 1 can do the job in 13/5 days
In one day Clerk 1 can do 1/ 13/5 or 5/13 of the job
Clerk 2 can do the job in 5/3 days
In one day Clerk 2 can do 1 / 5/3 or 3/5 of the job

(Note that "the job" = processing 350 papers; the 350 is not actually used in the computation at all!)

Set up the equation
Processing 350 forms represents completing 100% of the job or completing 1 job.
Below is the equation in words and the equation with the values from above:
(portion of the job completed in one day by Clerk 1 + portion of the job completed in one day by Clerk 2) x (total number of days) = 1 complete job

Find the common denominator and add:

x = 1 1/64 (one and one sixty-fourth) or 1.01 days

Here is another example of this type of problem using simpler numbers.
Painter 1 can paint a fence in 2 days
Painter 2 can paint the same in fence in 5 days
How long will it take if they work together?
Using our formula from above:
Painter 1 can do the job in 2 days
In one day Painter 1 can do 1/2 of the job
Painter 2 can do the job in 5 days
In one day Painter 2 can do 1 /5 of the job
Set up the equation:

Find the common denominator and add:

x = 1 3/7 (one and three sevenths)or 1.42 days(about a day and a half)