Question

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

Answer 1

The number of machines to complete job in 2 hours is 6.

Explanation:

Using the relation of the rate of each one machine and knowing that adding up both rates.

1. 
   `Rate R +Rate S= Rate total`

Rate R =
`(x)/(36)` 'x' is the job

Rate S =
`(x)/(18)` 'x' is the job

So, using the equation of rates

`Rate total =(x)/(36) + (x)/(18)`

Rate total is going to be a job in 2 hours so =
`(1)/(2)`

`(1)/(2) = (x)/(36)+(x)/(18)` adding up

`(1)/(2)= x*(3)/(36)` factoring the x

`(1)/(2)= x*(1)/(12)` simplifying

x=
`(12)/(2) \\`

x= 6