Problem Solving

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

using work formula to find the time it takes for both machines to do the same work:

(18*36)/54=12 hrs for both machines to complete the job

2 hrs is 6 times faster so the company needs 6 of each to do it in 12hr.

Answer C.

xilef wrote:using work formula to find the time it takes for both machines to do the same work:

(18*36)/54=12 hrs for both machines to complete the job

2 hrs is 6 times faster so the company needs 6 of each to do it in 12hr.

Answer C.

Can you give more explanation for the last step please? Thanks!

It takes both working together (one of each machine) to do the job in 12hrs. The company used the same number of each type of machine to do the job in 2 hours, which is 6 times faster than the the time it takes one of each machine to do the job, therefore, company used 6 of each.

xilef wrote:It takes both working together (one of each machine) to do the job in 12hrs. The company used the same number of each type of machine to do the job in 2 hours, which is 6 times faster than the the time it takes one of each machine to do the job, therefore, company used 6 of each.

thanks!

another way to look at things...

R does 1/36 the job

S does 1/18 the job

R+S = 1/12 the job or 12 hours to do 1 job

you want to do it in 2 hours....

so you you'll 12/2 = {6 machines each.}

1/36 + 1/18 = 1/12 so together they can do 1 job in 12 hours. Then, I set up the following equation:

2/1/12 = x/1/2 [translation: if 2 machines complete 1 job in 12, then how many machines will complete 1 job in 2 hours?]

24 = 2x

x = 12 machines, 6 of each type.

This is an interesting problem which can be solved in another way(rather a cryptic way). Thought of sharing this.
let the n be the number of machines.
We know the rates of the machines as 1/36 and 1/18.
Both working together for 2 hrs will do
2/36 + 2/18 amount of work.
Now we know n machines finished the work in 2 hrs.
So the equation will be
n*(2/36 + 2/18) = 1 (=1 coz the work got completed).
(This is the famous Logitech approach)

solving n = 6

HT Helps