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

Answer:

6 machines of each type  were used

Step-by-step 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 = $\frac{1}{36}$

thus,

the job completed in 1 hour by x number of type R = $x\times\frac{1}{36}$

similarly,

the job completed in 1 hour by S = $\frac{1}{18}$

thus,

the job completed in 1 hour by x number of type S = $x\times\frac{1}{18}$

Now,

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

Therefore, job completed in 1 hour = $\frac{1}{2}$

also,

$x\times\frac{1}{36}+x\times\frac{1}{18}$ =  $\frac{1}{2}$

or

$x\times(\frac{18+36}{36\times18})$ =  $\frac{1}{2}$

or

$x\times(\frac{54}{648})$ =  $\frac{1}{2}$

or

$x\times(\frac{1}{12})$ =  $\frac{1}{2}$

or

x = 6

Hence,

6 machines of each type  were used