swerve wrote: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 hrs 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 OA is C
Source: GMAT Prep
We have a combined worker problem for which we can use the following formula:
work (1 machine) + work (2 machine) = total work completed
Since we are completing one job, we can say:
work (1 machine) + work (2 machine) = 1
We are given that 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.
Thus, the rates for the two machines are as follows:
rate of machine R = 1/36
rate of machine S = 1/18
We are also given that the company used the same number of each type of machine to do the job in 2 hours. If we let x = the number of each machine used, we can multiply each rate by x and we have:
rate of x number of R machines = x/36
rate of x number of S machines = x/18
Finally, since we know some number of R and S machines worked for two hours, and since work = rate x time, we can calculate the work done by each type of machine.
work done by x number of R machines = 2x/36 = x/18
work done by x number of S machines = 2x/18 = x/9
Now we can determine x using the combined worker formula:
work (machine R) + work (machine S) = 1
x/18 + x/9 = 1
x/18 + 2x/18 = 1
3x/18 = 1
x/6 = 1
x = 6
Alternate Solution:
Let's find how much time it would take to complete the job if one type R machine and one type S machine were used.
In one hour, type R can complete 1/36 and type S can complete 1/18 of the job. Combined, they complete 1/36 + 1/18 = 3/36 = 1/12 of the job. If the two machines can complete 1/12 of the job in one hour, they can complete the whole job in 12 hours.
Next, we notice that the job was completed in 2 hours, which is 1/6 of 12. Since time and number of machines is inversely proportional, the number of type R machine - type S machine pairs must be 6 times the number of one pair; i.e. there must be 6 such pairs. Therefore, 6 machines of type R were used.
Answer: C
