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?

Answer 1

6 machines of each type were used

Explanation:

Data provided in the question;

Time taken by R to complete a job = 36 hours

Time taken by S to completed the same job = 18 hours

Let the number of machines used be x for each

Now,

the job completed in 1 hour by R =
`(1)/(36)`

thus,

the job completed in 1 hour by x number of type R =
`x*(1)/(36)`

similarly,

the job completed in 1 hour by S =
`(1)/(18)`

thus,

the job completed in 1 hour by x number of type S =
`x*(1)/(18)`

Now,

Together time taken by x of each type to completed the job = 2 hours

Therefore, job completed in 1 hour =
`(1)/(2)`

also,

`x*(1)/(36)+x*(1)/(18)` =
`(1)/(2)`

or

`x*((18+36)/(36*18))` =
`(1)/(2)`

or

`x*((54)/(648))` =
`(1)/(2)`

or

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

or

x = 6

Hence,

6 machines of each type were used