Company C has a machine

[candace_washington1980]

Hi I,m new this website, I have several questions from the gmat test prep that I'm having difficulty with. I was able to get this one correct but I'm not sure how I got it. Please help.

Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?

A. 50
B. 45
C. 30
D. 25
E. 20

The answer is C, but how?

[furtadovinod]

Hi I,m new this website, I have several questions from the gmat test prep that I'm having difficulty with. I was able to get this one correct but I'm not sure how I got it. Please help.

Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?

A. 50
B. 45
C. 30
D. 25
E. 20

The answer is C, but how?

I guess there are number of ways to work this out. My way is

Old machine processes 100 units of the product in 5 hrs.

Therefore, it produces 20 units per hr.

Old machine + New machine must produce 100 units in 2 hrs.
Therefore, 50 units per hr.

Since old machine produces 20 units per hr, the new machine must produce at 30 units per hr to get a total of 20+30=50 units per hr.

[candace_washington1980]

Well this is how I worked it.

Machine 1 Machine 2 Both machines
rate=100 x rate=100
5 2
rate= 20 rate= 50

20 + x = 50
x = 30

Is this correct or did I get lucky because the numbers worked out?

[RenzoA271]

I approached it this way. I'm not sure if it's totally right, but I got the right answer. Please correct if I'm wrong

Machine C:

w=rt
100= r5
20=r

New Machine:

100=(20+r)2
50=20+r
30=r

[Sage Pearce-Higgins]

That working is totally correct. However, to make sure that you're able to tackle similar questions in the future, take time to understand each of the steps you made. The first part is probably clear: you worked out the rate of the existing machine. However, the next equation is trickier. Explain to yourself: "Where does 20 + r come from?".