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widgets problem

by gmat009 » Tue Oct 07, 2008 8:22 pm
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?
A. 4
B. 6
C. 8
D. 10
E. 12
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by cramya » Tue Oct 07, 2008 8:50 pm
I get 12 as the answer. Whats the OA?
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by cramya » Tue Oct 07, 2008 8:56 pm
Let z be the number of days Y takes to produce w widgets
X takes z+2 days

X's rate = w / z+2 and Y's rate is w/z

Combined rate they produce 5w/4 in 3 days i.e
w/z+2 + w/z
= 2w(z+1)/z (z+2)

Combined rate * nof of days * no of machines(which is 1 since they work together) = work(5w/4)

i.e. 2w(z+1)/z (z+2) * 3 * 1 = 5w/4

Solving for z we get 4 which is Y's days so X's rate is z+2 = 6 days

But this 6days is for producing w widgets by X so to produce 2w widgest it takes 2 * 6 = 12 days

E)
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by 4meonly » Fri Oct 10, 2008 7:45 am
I dont know how to get 12 as answer

I used the same logic as cramya but got another answer
2w(z+1)/z (z+2) * 3 * 1 = 5w/4
6w(z+1)/z (z+2) = 5w/4

24w(z+1) = 5wz(z+2)
24wz+24w = 5wz^2 + 10wz
w(5z^2 -14z + 24) = 0
w(z-12)(z-2) = 0
as w is not equal to 0
z cannot be 12 because we have no such answers
z=2
Rate X = w/4 to make w X needs 4 days, to make 2w X should work 8 days

I think C
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by amitansu » Fri Oct 10, 2008 9:35 pm
Yes, it should be 'C'.

Same logic where i got 'C' as the ans.


Amit
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by cramya » Fri Oct 10, 2008 10:03 pm
w cancels out

So we are left with
5z^2-14z-24 = 0

5z(z-4)+6(z-4) = 0

z = 4 is the only solution that applies since the other valueof z will be negative

Hope this helps
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by cramya » Fri Oct 10, 2008 10:05 pm
Adding one more step in bold

w cancels out

So we are left with
5z^2-14z-24 = 0

5z^2-20z+6z-24 = 0

5z(z-4)+6(z-4) = 0

z = 4 is the only solution that applies since the other valueof z will be negative

Hope this helps[/b]
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by amitansu » Fri Oct 10, 2008 10:26 pm
yes...the no. of days would be 4
but X takes 2 days more so 6 days and then to produce 2wigets X should take 12 days not 8 days.

I did a mistake just by taking 4 days :(

12 is the right ans.


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by 4meonly » Sat Oct 11, 2008 1:48 am
4meonly wrote: w(5z^2 -14z + 24) = 0
w(z-12)(z-2) = 0
Here is my mistake
I forgot about 5
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