Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 1w widgets?
Choose the correct choice from the following choices
A) 4
B) 6
C) 8
D) 10
E) 12
Let Y produce w widgets in y Days   Hence, in 1 day Y will produce w/y widgets.   Also, X will produce w widgets in y+2 days (given, X takes two more days)   Hence, in 1 day X will produce w/y+2 widgets.   Hence together X and Y in 1 day will produce {w/y + w/y+2} widgets.   Together X and Y in 3 days will produce = 3 * [{w/y + w/y+2}] widgets.   It is given that in 3 days together they produce (5/4)w widgets.   Equating, 3 * [{w/y + w/y+2}] = (5/4)w   Take out w common and move 3 to denominator of RHS   w{1/y + 1/(y+2)} = (5/12)w   Canceling w from both sides   {1/y + 1/(y+2)} = 5/12   2y+2/y(y+2) = 5/12   24y+24=5y^2 + 10y   5y^2-14y-24=0   5y^2-20y+6y-24=0   5y(y-4)+6(y-4)=0   (5y+6)+(y-4)=0   y=-6/5 or y=4   Discarding y=-6/5 as no of days cannot be negative   y=4   hence it takes Y, 4 days to produce w widgets.   Therefore, it will take X  (4+2)= 
<gadget id="calculator"> (4+2)</gadget>
<output>6</output>
6 days to produce w widgets.   Hence it will take X 1*6= 
<gadget id="calculator">1*6</gadget>
<output>6</output>
6 days to produce 1w widgets.   Answer : 6
<result>B</result>
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 1w widgets?