Machine X and Y produced...

[jellie]

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?
(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours.

Could someone explain how to solve this problem?
Would I need to use a rate chart for this?

[Guest]

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?
(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours.

So the question entails finding the number of hours it takes X to fill the entire lot.

X works for 4 hours and Y worked for 3 hours to fill the lot.

1) X produced 30 bottles per minute, thus 4 * 60 * 30 = 7200 bottles for 4 hours. However we do not know Y's rate to determine the number of bottles Y finished, and subsequently the time required by X to produce the total ## of bottles. Thus, insufficient

2. X produces twice as many bottles in 4 hours as machine Y in 3 hours
Assume Y produces b bottles, machine X produces 2b bottles
Total bottles produced: b + 2b = 3b in 7 hours

We know:
Machine X produces: 2b bottles -----> 4 hours
3b bottles can be produced in ----- > (4/2b) * 3b = 6 hours. Thus 2 is sufficient.

Answer B. Can you please confirm. Thanks !!

[Jellie]

Yup. Answer choice B is correct.

Thanks

[Jellie]

Just one quick question though. I don't understand the last step.


Machine X produces: 2b bottles -----> 4 hours
3b bottles can be produced in ----- > (4/2b) * 3b = 6 hours. Thus 2 is sufficient.


How do you go from knowing 3b to the last equation which yields 6 hours?

[Divya]

Just one quick question though. I don't understand the last step.


Machine X produces: 2b bottles -----> 4 hours
3b bottles can be produced in ----- > (4/2b) * 3b = 6 hours. Thus 2 is sufficient.


How do you go from knowing 3b to the last equation which yields 6 hours?

2) Machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours.
Using statement 2, I used a variable b for the ## of bottles Y produces in 3 hours.
Thus X produced 2b bottles in 4 hours
Total bottles produced by X and Y : b + 2b = 3b

Question is how long will X take to fill the lot by himself. In this case we need to find the time X will take to complete the entire work (3b) bottles by himself. You can use the work rate formula
W = R * T

Rate of x = 2b/4 ( since X produces 2b bottles in 4 hours)
Total work required : 3b
thus, 3b = 2b/4 * t
t = (3b * 4) /2b
t = 6

Hope this helps

[Aman_Gupta]

From the statement 2:

I assumed y to be the rate of bottle production for machine Y.

Forming the equation:

2y*4 + y*3 = 1

(1 is the total amount of work completed if we take the whole thing in fractions)

=> 8y+ 3y = 1
=> 11y = 1 => y = 1/11

hence, x = 2y = 2/ 11

Time = 1/ rate
=> x will take 11/2 hours = 5.5 hours to complete the job

The thread says that X takes 6 hours to complete the job.
Where am I going wrong with my approach?

I know for DS question my answer remains same but I won't be so lucky in PS questions.

[tim]

Right at the top:

2y*4 + y*3 = 1

You're assuming here that x's rate is twice that of y, which is not stated anywhere in the problem. In fact, we have evidence that this is definitely NOT the case. Look closely at the information that is given about x and y.