machines R and S

Xbond wrote:Hi

How resolve it ? OA is C

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type
of machine to do the job in 2 hours, how many machines of type R were used ?

A) 3
B) 4
C) 6
D) 9
E) 12

The combined time it takes two workers to do a job is the product of the individual times of the workers divided by the sum of the individual times:

Tab = Ta * Tb/(Ta + Tb)

Tab = 36*18/(36 + 18) = 36*18/54 = (6*6*9*2)/(6*9) = 6*2 = 12 hours.

So, if there was one R and one S, it would take them 12 hours to complete the job. We are told, however, that it took them only 2 hours to do the job (and that the number of them is equal). So, they actually did the job 12/2 = 6 times as fast as they would have had there been one machine of each type. So, there must be 6 machines of each type.

This is exactly how I solved it too.

Xbond wrote:Hi

How resolve it ? OA is C

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type
of machine to do the job in 2 hours, how many machines of type R were used ?

A) 3
B) 4
C) 6
D) 9
E) 12

Great solutions so far. This is a question on which common sense/backsolving also works great.

Before we backsolve, let's narrow down the choices with logic:

If we used all type S machines, it would take 18/2 = 9 total machines. Half of 9 is 4.5, so the answer must be more than 4.5: eliminate A and B.

If we used all type R machines, it would take 36/2 = 18 total machines. Half of 18 is 9, so the answer must be less than 9: eliminate D and E.

(I took half of each number because the question is asking only about one type of machine, and we're using the same number of each, so we want half of the total # of machines used.)

Well heck, only C is left, we don't even have to do any plugging in!