Running at their respective constant rates, Machine X takes

[mpopatia]

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if two machines together produce 5/4w 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

OA - E

I understand the OA method which uses algebra: 3(w/d + w/d+2) = 5/4w and solves to be 6, and then 2w = 12. However I attempted to use the RTW chart and got stuck! Is there a way to pick numbers for the variables and use the RTW chart for this type of problem?

[Viswanathan.harsha]

Can you please work out the algebra for the given problem? I am having difficulty getting w=6. Is this problem from gmat prep?

[rash.patil]

[edit: there's a mistake in this post; it should be (2t - 2), not (2t - 1), where the green-colored part is (and in any subsequent steps).]

Let T total number of days taken by machine X to produce W widgets.
Then Work done by x is 1 day is W/T

Work done by machine y in 1 day = W/(T - 2).

Combined work done in 3 days = 3( W/T + W/(t-2) )

= 3W( 2T-1 ) / (T- 2) which is equal to 5W/4
So equating the two equations we get

12( 2T - 1 ) = 5T( T - 2)
24T - 12 = 5T2 - 10T
5T2 - 32T + 12 = 0
(T-6) (5T+2) = 0.
Which gives T = 6.
So no. of days to produce 2W widgets = 2T = 12.
Ans: E

[Viswanathan.harsha]

I believe it is supposed to be 12 (2T-2)=5T(T-2)

This gives you 5T^2-34T+24=0

Giving you t=6

[mschwrtz]

That's right Viswanathan.harsha

[ayush.sharma]

Guys - I get stuck as well.
The difference is that you are taking one value to be
D days and then Y to be D-2.


But what if you take y to be D days and x to be D+2.
As given in the question ( Machine X takes 2 days longer)
So I put Machine Y takes D days
and Machine X takes 2+D days.........

By doing that I get stuck at a quadratic that does not make sense :
5d^2 -14d-24=0


I cant see why my approach is wrong.
Any help ?

[SRK]

Even i am facing the same issue as ayush. Could some one please help?

[ayush.sharma]

Got it.
The equation is correct.
5t^2 -14t-24=0
When ever I see the co-efficient of t^2>1 - I just go for
roots of quadratic =

(-b +or - sqrt ( b^2-4ac))/2a


The mistake I was making before was that the value of c in this equation is not 24 but -24. and that will give one of the roots as 4 and that is what we were looking for.

Does anyone have a better way to deal with this revere foil quadratic eq with coeff x >1?

thanks- hope that helped

[tim]

cool. let us know if you have any other questions about this one..

[shubham_sagijain]

I think insted of solving the equation, it is much better to substitute the values in the eqn and check.

D --> Number of days

1/D - rate of Y
1/(D+2) - rate of X

we get 3 (1/D + 1/(D+2)) = 5/4.

Now, just substitute D = 4 and see whether the eqn is satisfied.
So, 4 + 2 = 6 days - No. of days taken by X to produce W widgets.
Just multiply by 2 to get the number of days to produce 2 W widgets.
2* 6 = 12..so E is the answer :)

Thanks,
Shubh

[RonPurewal]

that's a nice way to do it.

[lim.aguskurniawan]

Hi , I somehow do not get the same answer. can anybody advise? what is wrong with me equation.

here is the logic:
suppose x can finish the widget in x day,
then y can finish the widget in x-2 days.

given that if 2 machines X and Y can finish 5/4 widgets in 3 days, in order to finish 2 widgets, machine x annd Y together will take 24/5 days.

so putting all information into equation, we get:
1/x + 1/(x-2)=1/(24/5)
1/x+1/(x-2)=5/24
5x^2 -58x+48=0

the equation can not be solved :). anybody please advise what is wrong with my equation.

thanks

[tim]

you're trying to produce 2w widgets. if x takes 2 days longer to produce w widgets, it will take *4* days longer to produce 2w widgets. try the problem again with this information, and i think you'll get it..

[jean.spellman]

Hi all,

Forgive me if this is a stupid question, but how do you get from:
3( W/T + W/(t-2) )

to

3W( 2T-1 ) / (T- 2)? (see rash.patil answer from 2010)

The answer(s) otherwise make sense, but I'm getting stopped at this step. Thank you.

[RonPurewal]

Hi all,

Forgive me if this is a stupid question, but how do you get from:
3( W/T + W/(t-2) )

to

3W( 2T-1 ) / (T- 2)? (see rash.patil answer from 2010)

The answer(s) otherwise make sense, but I'm getting stopped at this step. Thank you.

i can't tell whether this question is ...
... (i) "i understand what i'm supposed to do here, but i don't see where that answer is coming from"
or
... (ii) "i don't have any idea what process to use at this point".

so, i'll answer both.

----------------

if it's (i):

well, you don't get there.
check out the second post, in which another poster calls out the mistake. (i've now edited the top post to make clear that a mistake has been made.)

----------------

if it's (ii):
the poster is attempting to add two fractions by creating a common denominator.

* first, factor out 3w to give 3w(1/t + 1/(t - 2)). that 3w is just going to sit out there for the rest of the game; the rest of the action is inside the parentheses.

* the common denominator is t(t - 2), so multiply the left-hand fraction by (t - 2) on the top and bottom, and multiply the right-hand fraction by t on the top and bottom.

* then add the resulting fractions, which will now have the same denominator.
you'll get (t - 2 + t) / (t(t - 2)), or (2t - 2) / (t(t - 2)).