Collection of work/rate problems?

****28.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 4hours as machine Y produced in 3 hours.

let X = time it takes Machine X to fill lot
let Y = time it takes Machine Y to fill lot

4*(1/X) + 3*(1/Y) = 1

From Statement 1 we know the total number of bottles made in four hours by Machine X

NOT SUFFICIENT

From Statement 2 we know that Machine Y produced half the total mentioned above in three hours

Using this info, we can determine how long it would take Machine X to fill the lot:

Total # of bottles * (1 hr / (30*60) bottles) = Number of Hours it would take Machine X to fill the lot

ANSWER: C. Both statements together are sufficient***

11.6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

I think I saw this one in the first PowerPrep Test:

This is a simple two equation problem:

let x = the number of additional machines needed to complete the job in 8 days
let y = the rate for one machine to complete the job

Equation 1:

Rate * Time = Work
6*y*12 = 1 job

Equation 2:

(6+x)*y*8 = 1 job

so...
y = 1/(6*12)
(6+x)*(1/(6*12))*8 = 1
x = 3

15. working together at their constant rates , A and B can fill an empty tank to capacity in1/2 hr.what is the constant rate of pump B?
1) A's constant rate is 25LTS / min
2) the tanks capacity is 1200 lts.

From the original statement we know that:
1/A + 1/B = 1/(1/2)

From Statement 1 we can plug in and find B: SUFFICIENT

Statement 2 is completely unnecessary:

ANSWER: A. Statement 1 alone is sufficient

I don't think this is correct. We know that the rate of A and B = 1/30 of a tank per minute (given in the stem). If A had said that pump A fills X OF THE TANK per minute, then it'd be sufficient alone since A + B = rate of A + rate of B and can solve for rate of B given that we know A. However, this gives it to us in units other than what the stem gave us, so we need to know the tank's capacity. Statement 2 gives us the capacity, so if we use them in conjunction, we can solve the problem. Should be C, not A, IMO.

Yes, the answer to this question is C not A.

Working together at their constant rates, A and B can fill an empty tank to capacity in 1/2 hours. What is the constant rate of pump B?

\(rate*time=job\).

We are told that \((A+B)*30=C\), where \(A\) is the rate of pump A in lts/min, \(B\) is the rate of pump B in lts/min and C is the capacity of the tank in liters.

Question: \(B=?\)

(1) A's constant rate is 25 LTS / min --> \(A=25\) --> \((25+B)*30=C\) --> clearly insufficient (two unknowns), if \(C=1200\), then \(B=15\) but of \(C=1500\), then \(B=25\).

(2) The tanks capacity is 1200 lts. --> \(C=1200\). \((A+B)*30=1200\) --> \(A+B=40\). Also insufficient.

(1)+(2) \(A=25\) and \(A+B=40\) --> \(B=15\). Sufficient.

Answer: C.

Discussed here: working-together-at-their-constant-rates-a-and-b-can-fill-97316.html

28.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 4hours as machine Y produced in 3 hours.

Ans C
With Statement 1 - we cant find out the total work
With Statement II - we can only express the speed of one machine in terms of the other

Both statements are needed for the complete picture

I think B would be the correct answer.

Let machine y produce = Y bottles in 3 hrs ( rate = y/3 bottles/hr)
Let machine x produce = 2Y bottles in 4 hrs ( rate = 2y/4 = y/2 bottles/hr)

Total no of bottles produced by both x and y = 3Y.

So, time machine x takes to produce 3Y bottles is = 3Y/(Y/2) = 6hrs.

Hello,

Can I have the solution for 23 please? I am not sure if I understand the question to be honest though. Are we looking for the number of days that it would take Michael to finish the whole project seperately of after the 12 days that they have been working together? Or neither of the two..?

Thank you.