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?

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 !!

Yup. Answer choice B is correct.

Thanks

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?

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