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

ANS 12..

Suppose machine Y produces w widgets in d days

so, X produces same in d+2 days

In 1 day Y produces w/d and X produces w/(d+2) widgets

Working together they will produce w/d + w/(d+2) = [2w(d+1)]/[d(d+2)] widgets in 1 day

in 3 days they produce 3*[2w(d+1)]/[d(d+2)] = 5w/4

Solve to get d =4

x produces w widgets in 4+2 = 6 days

so, 2w widgets will be produces in 12 days

OA???

OA is E

i realize this is an old post but could someone show me the actual calculation that goes from this step -

in 3 days they produce 3*[2w(d+1)]/[d(d+2)] = 5w/4

to this step -

Solve to get d =4

i seem to be making a simple error somewhere...

Let the no. of days that Y takes is d

then no. of days that X takes will be d+2

X's rate = w/(d+2)
Y's rate = w/d

[w/d + w/(d+2)] * 3 = 5w/4

(w(d+2) + wd) /d(d+2) = 5w/12

wd + 2w + wd = 5wd(d+2)/12

24w(d+1) = 5wd(d+2)

24(d+1) = 5d(d+2)

24d + 24 = 5d^2 + 10d

5d^2 -14d - 24 = 0

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

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

d=-6/5 or 4

time cannot be negative, hence d=4

X produces w in d+2 = 4+2

2w will be produced in 6+6 = 12 days

Hope this helps.

anybody know the source of this problem? or think its realistic gmat problem?

netigen wrote: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

This question is from GMATPrep. An efficient way to solve this problem is to plug in the answer choices.

Let w=12.
In 3 days, X and Y need to produce 5/4*w = 5/4*12 = 15 widgets.
The answer choices represent the time for X to produce 2w=24 widgets.

Answer choice C: 8 days for X to produce 24 widgets
Thus, X produces 12 widgets in 4 days.
Since X takes 2 days longer, Y produces 12 widgets in 4-2=2 days.
Rate for X = w/t = 12/4 = 3/day.
Rate for Y = w/t = 12/2 = 6/day.
Combined rate for X+Y = 3+6 = 9/day .
Work completed in 3 days = r*t = 9*3 = 27 widgets.
Incorrect: almost DOUBLE the required number of widgets (15) is being produced.
Thus, X and Y need to work MUCH MORE SLOWLY, implying that the time for X to produce 24 widgets must be MUCH LONGER.

Answer choice E: 12 days for X to produce 24 widgets
Thus, X produces 12 widgets in 6 days.
Since X takes 2 days longer, Y produces 12 widgets in 6-2=4 days.
Rate for X = w/t = 12/6 = 2/day.
Rate for Y = w/t = 12/4 = 3/day.
Combined rate for X+Y = 2+3 = 5/day.
Work completed in 3 days = r*t = 5*3 = 15 widgets. Success!

The correct answer is E.

GMATGuruNY wrote:

netigen wrote: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

This question is from GMATPrep. An efficient way to solve this problem is to plug in the answer choices.

Let w=12.
In 3 days, X and Y need to produce 5/4*w = 5/4*12 = 15 widgets.
The answer choices represent the time for X to produce 2w=24 widgets.

Answer choice C: 8 days for X to produce 24 widgets
Thus, X produces 12 widgets in 4 days.
Since X takes 2 days longer, Y produces 12 widgets in 4-2=2 days.
Rate for X = w/t = 12/4 = 3/day.
Rate for Y = w/t = 12/2 = 6/day.
Combined rate for X+Y = 3+6 = 9/day .
Work completed in 3 days = r*t = 9*3 = 27 widgets.
Incorrect. We need much less work to get done, so the time for X must be much longer.

Answer choice E: 12 days for X to produce 24 widgets
Thus, X produces 12 widgets in 6 days.
Since X takes 2 days longer, Y produces 12 widgets in 6-2=4 days.
Rate for X = w/t = 12/6 = 2/day.
Rate for Y = w/t = 12/4 = 3/day.
Combined rate for X+Y = 2+3 = 5/day.
Work completed in 3 days = r*t = 5*3 = 15 widgets. Success!

The correct answer is E.

NICE

Hello,

Can anyone please explain how to get from:
w/d + w/(d+2)

To

[2w(d+1)]/[d(d+2)]?

Ty!