GMAT Prep - Rates

Hi,

This question is not so bad if you convert the rates into whole numbers and then just test the answer choices.

We are not told how big the job is, so you can make up a job that is a multiple of the two rates (18 and 36). So the job can be 36 units.

Since R can complete the job in 36 hours, R's rate is 1 unit/hour. Likewise, since S can complete the job in 18 hours, S's rate is 2 units/hour.

If the entire job was completed in only 2 hours, as the question tells us, the combined rate for the entire job of 36 units was 18 units per hour. Thus, we want to find out how many S and R machines working together can work at a combined rate of 18 units per hour, where S and R each has the same number of machines running.

Here, you can just test the answer choices. If you are testing the answer choices, it is best to start with (C), because if (C) is wrong you can tell whether you need a bigger or smaller number.

(C) = 6. If 6 R machines were working at a rate of 1 unit per hour, they would produce units at a combined rate of 6 units per hour. If 6 S machines worked at a rate of 2 units per hour, they would produce units at a combined rate of 12 units per hours. Thus, the combined rate of 6 R machines and 6 S machine working together is, indeed, 18 units per hour -- which is what we are looking for.

Cheers,

I think picking numbers might take me too long...is there something wrong with the method I attempted?

Machine A takes 36 hours
Machine B takes 18 hours.

Let the work is 72 units.
So rate of A is 2 unit/hour
rate of B = 4 unit/hour

combined rate = 6 unit/hour
so, to finish the work, they need 12 hours(72/6).
to finish the work in two hours, they need to do 36 unit/hour
So, amount of unit they need is 6*6.
so they need 6 of each type.

But is my method incorrect?

I did the following way :
Lets say x machines of machine R and machine S are used to do the work in 2 hours. The equation becomes :

x/36 + x/18 = 1/2
x/18 + x/9 = 1
3x = 18
x = 6

rosh26 wrote:Ok here is how I attempted this problem, want to know if my logic is correct

R's rate: 1/36
S's rate: 1/18

1/36x + 1/18x = 1/2

x = 6

I think I just got lucky with this one...

Do you have to go one step furthur to say 36 hours / 6 = 6 ???

Not sure...

I solved this problem the exact same way. The reason I used x to multiply the rates of each machine is because the question stem said the same number of each type of machine was used.. However my way of solving was very different from Shrindidhi because I put the x on the bottom.

Which is the correct method for setting up the equation. and Why?

x/36 + x/16 = 1/2

or

1/36x + 1/18x = 1/2

How did u solve the equation?

anniev2 wrote:

rosh26 wrote:Ok here is how I attempted this problem, want to know if my logic is correct

R's rate: 1/36
S's rate: 1/18

1/36x + 1/18x = 1/2

x = 6

I think I just got lucky with this one...

Do you have to go one step furthur to say 36 hours / 6 = 6 ???

Not sure...

I solved this problem the exact same way. The reason I used x to multiply the rates of each machine is because the question stem said the same number of each type of machine was used.. However my way of solving was very different from Shrindidhi because I put the x on the bottom.

Which is the correct method for setting up the equation. and Why?

x/36 + x/16 = 1/2

or

1/36x + 1/18x = 1/2

The FIRST method that you have laid out is absolutely not correct.

R: rate at which 1 m/c works= 1/36
rate at which n m/c will work= n/36 (not 1/36n)

S: rate at which 1 m/c works= 1/18
rate at which n m/c will work= n/18

Combined rates completes the work in 2 hrs.
rate at which R+S works = 1/2

n/36 + n/18 = 1/2 and solve. Hope it's clear.

Thanks kanha81,


It gave me a weird face when I saw their equation.