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Question 201997: Respected sir,
plz help me to solve this arith problem...
1] 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 2w widgets?
waiting for yurs reply sir.
Thank u.
Regards
Binita.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of days it takes Y to produce w widgets
Then Y produces at the rate of w/x widgets per day
x+2=amount of days it takes X to produce w widgets
Then X produces at the rate of w/(x+2) widgets per day
Together the two machines work at the rate of w/x + w/(x+2)=(w(x+2)+wx)/x(x+2) widgets per day
But we are told that the two machines together work at the rate of (5/12)w widgets per day ((5/4)w widgets in 3 days =(5/12)w widgets per day))
Now our first equation to solve is:
(w(x+2)+wx)/x(x+2)=(5/12)w multiply each side by x(x+2)
w(x+2)+wx=(5/12)wx(x+2) simplify
wx+2w+wx=(5/12)wx^2+(10/12)wx
2wx+2w=(5/12)wx^2+(10/12)wx multiply each term by 12
24wx+24w=5wx^2+10wx subtract 24wx and 24w from each side
5wx^2-14wx-24w=0 Assuming w is not equal to zero, divide each term by w
5x^2-14x-24=0 quadratic in standard form
If we use the quadratic formula to solve, we get:
x=(14+-26)/10 or
x=40/10=4---number of days it takes Y to produce w widgets
and
x=-14/10----Disregard. Days in this problem are positive
Now for X
x+2=amount of days it takes X to produce w widgets or
x+2=4+2=6----number of days it takes X to produce w widgets
So X produces 2w widgets in 6*2=12 days--------------ans
Another way to look at it: X produces at the rate of w/(x+2) widgets per day or
w/(4+2)=w/6 widgets per day so in 12 days X produces (w/6)*12=2w widgets
Hope this helps---ptaylor
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