Problem Solving

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

I get 12 as the answer. Whats the OA?

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)

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

Yes, it should be 'C'.

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


Amit

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

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]

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.


Amit

4meonly wrote: w(5z^2 -14z + 24) = 0
w(z-12)(z-2) = 0

Here is my mistake
I forgot about 5