SOLUTION: Christy can finish typing one letter ahead of John by 1 min. Together they can finish 27 letters in 60 mins. How long does it take for each to finish typing one letter?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Christy can finish typing one letter ahead of John by 1 min. Together they can finish 27 letters in 60 mins. How long does it take for each to finish typing one letter?      Log On


   

Question 1168933: Christy can finish typing one letter ahead of John by 1 min. Together they can finish 27 letters in 60 mins. How long does it take for each to finish typing one letter?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Time for john to write 1 letter, j.
Time for Christy the same leter, j-1.

%281%2Fj%2B1%2F%28j-1%29%2960=27 for RT=W, rate multiplied by time is how much work done.

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%281%2Fj%2B1%2F%28j-1%29%29%2A20=9
%28j-1%2Bj%2920=9%28j%5E2-j%29
20%282j-1%29=9j%5E2-9j
40j-20=9j%5E2-9j
9j%5E2-49j%2B20=0
j=%2849%2B-+sqrt%2849%5E2-4%2A9%2A20%29%29%2F%282%2A9%29
j=%2849%2B-+sqrt%281681%29%29%2F%282%2A9%29
j=%2849%2B-+41%29%2F%282%2A9%29
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system%28cross%28j=4%2F9%29%2COR%2Chighlight%28highlight%28j=5%29%29%29
One of these will not work but the other does work.