SOLUTION: PLEASE HELP ME !!!! Pat and Jen volunteer at the library. Pat can shelve a full cart of books 10 minutes faster than Jen. if they work together, they can shelve a full cart in 70

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Question 786122: PLEASE HELP ME !!!!
Pat and Jen volunteer at the library. Pat can shelve a full cart of books 10 minutes faster than Jen. if they work together, they can shelve a full cart in 70 minutes. How long does it take Jen to shelve a full cart by herself (give an exact answer and an answer rounded to the nearest minute)?
Answer by xinxin(76) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is tricky because you may mistakenly add their individual working time to the total of 70 minutes.
Suppose Jen needs X minutes to shelve a full cart by herself, and the number of books on the cart is A, then:
(A/(X-10) + A/X ) * 70 = A
X^2 -150X +700 =0
Solve for X, get X = 145 or X = 5. Well if X is 5 then Pat will have a negative working time. Thus Jen uses 145 minutes to shelve a full cart.