Question 1199268
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Chris can do it in 3/4 as many days as Araceli can:
let 4x = days Araceli takes
then 3x = days Chris takes<br>
Jay can do it in 2/3 as many days as Chris can:
then 2x = days Jay takes<br>
The fraction of the job Araceli does in 1 day is 1/(4x)
The fraction of the job Chris does in 1 day is 1/(3x)
The fraction of the job Ray does in 1 day is 1/(2x)<br>
Together in 1 day the fraction of the job the three together do is<br>
{{{1/(4x)+1/(3x)+1/(2x) = 3/(12x)+4/(12x)+6/(12x) = 13/(12x)}}}<br>
That means the number of days it takes them to do the job together is {{{12x/36}}}<br>
The number of days they take to do the job is 36/13, so<br>
36/13 = 12x/13 --> x = 3<br>
ANSWERS:
# of days for Araceli alone = 4x = 12
# of days for Araceli alone = 3x = 9
# of days for Araceli alone = 2x = 6<br>