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. 3B. 4C. 6D. 9E. 12

Answer 1

Answer: C. 6

Therefore, 6 machine R was used.

Explanation:

Given;

Time taken for machine R = 36 hours

Time taken for machine S = 18 hours

The fraction of work completed by machine R and S in 1 hour is ;

R = 1/36

S = 1/18

Let n represent the number of each type of machine used to do the job.

Time taken for n machine R and S is 2 hours.

The fraction of job completed by n Machine R and S is;

n(R +S) = 1/2

Since R = 1/36 and S = 1/18

n(1/36 + 1/18) = 1/2

n = 1/2/(1/36 + 1/18)

n = 6

Therefore, 6 machine R was used.