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,
David Stoll
The Princeton Review
