Question 965964
After encoding the manuscript for 5 days, Agnes asked the help of her friend Xander. 
Together they finished the entire manuscript in 4 days. 
Had Xander joined in a day after Jane,the whole encoding work would have been finished in 7 days.
 How long would it have taken Agnes to encode the manuscript alone?
:
let a = time for Agnes to do the job alone
let x = time for Xander to do it
:
Let the completed job = 1, write an equation for each scenario
"After encoding the manuscript for 5 days, Agnes asked the help of her friend Xander. Together they finished the entire manuscript in 4 days. '"
Agnes worked 9 days
{{{9/a}}} + {{{4/x}}} = 1
:
Xander joined in a day after Jane,the whole encoding work would have been finished in 7 days. 
{{{7/a}}} + {{{6/x}}} = 1
:
multiply the 1st equation by 3, the 2nd equation by 2
{{{27/a}}} + {{{12/x}}} = 3
{{{14/a}}} + {{{12/x}}} = 2
--------------------------------Subtraction eliminates x, find a
{{{13/a}}} = 1
a = 13 days for Agnes to do the job alone
:
:
To confirm this we have to find how long it take Xan alone
{{{9/13}}} + {{{4/x}}} = 1
multiply by 13x, cancel the denominators
9x + 13(4) = 13x
52 = 13x - 9x
52 = 4x
x = 52/4 
x = 13 days for Xan also
:
Check it in the 2nd equation with these values
{{{7/13}}} + {{{6/13}}} = 1
{{{13/13}}} = 1