widgets

[shibal]

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?

oa 12

[Sid_Backlash]

As X takes 2 days more to produce w widgets than Y takes,

we have Y=X+2

Working together, X and Y take 3 days to make 5/4w widgets...

Therefore, together they take 12/5 days to make w widgets..

so now the eqn. is

1/X + 1/Y = 5/12

=> 1/X + 1/(X+2) = 5/12

Solving, u get X = 4..

So X takes 4 days to make w widgets alone...

Hence for 2w widgets, X will take 8 days...

[Ad_Astra_Per_Aspera]

IMO the answer should be 12.

y takes d days to produce w so it follows that x takes d+2 days to produce w.

machine y working alone produces w/d and machine x produce w/(d+2)

working together for 3 days:

w/d + [w/(d+2)] = 5w/12

5w/12 = 2w(d+1) / [d(d+2)]

5d^2 - 14d - 24 = 0

divide by 5 throughout

d^2 - (14/5)d - 24/5 = 0

d^2 + (6/5)d - 4d - 24/5 = 0

d(d + 6/5) - 4(d + 6/5) = 0

(d - 4) (d + 6/5) = 0

d = 4 or d = -6/5

so d = 4

so x takes 6 days to produce w which means it takes 2*6 = 12 days to produce 2w

[Sid_Backlash]

Yes Ad... u re right..

I reversed the variables in my equation..

Y = X -2 and not X + 2 as I had posted...

and yes.. the answer comes to 12

[truplayer256]

If Machines X and Y can produce 5w/4 widgets in 3 days, then they can produce 5w/12 widgets a day. To find how many days it'll take them to produce 2w widgets, we can do the following:

5w/12(d)=2w

d= number of days it'll take Machines X and Y to produce 2w widgets.

d=2w*12/5w=24/5 days.

We know that it takes Machine X 2 days longer to produce w widgets than the time it takes Machine Y. It'll take Machine X 4 days longer to produce 2w widgets than the time it takes Machine Y to produce them.

Let's form an equation from the information that's been given to us:

Please be sure to keep this formula in mind when dealing with these kinds of questions

1/Rate of Maching X alone+1/ Rate of Machine Y alone= 1/ Rate of Machines X and Y together.
Let's say that it takes Machine Y y days to produce 2w widgets.

1/y+4+1/y=5/24

2y+4=5/24(y^2+4y)

2y+4=5y^2/24+5y/6

7y/6=5y^2/24-4

5y^2/24-7y/6-4=0

5y^2-28y/24=4

96=5y^2-28y

5y^2-28y-96=0

y=8

Since it takes Machine X 4 days longer to produce 2w widgets, it'll take 8+4 or 12 days for it to produce that many widgets.