Question 246035
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

{{{(5/13 +3/5)x = 1}}}
Find the common denominator and add:
{{{(25/65 + 39/65)x = 1}}}
{{{(64/65)(x) = 1}}}
{{{x = 65/64}}}
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:

{{{(1/2 + 1/5)x = 1}}}
Find the common denominator and add:
{{{5/10 + 2/10)x = 1}}}
{{{(7/10)(x) = 1}}}
{{{x = 10/7}}}
x = 1 3/7 (one and three sevenths)or 1.42 days(about a day and a half)