SOLUTION: 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,t

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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
+ = 1
:
Xander joined in a day after Jane,the whole encoding work would have been finished in 7 days.
+ = 1
:
multiply the 1st equation by 3, the 2nd equation by 2
+ = 3
+ = 2
--------------------------------Subtraction eliminates x, find 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
+ = 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
+ = 1
= 1

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