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

Answer:

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

Step-by-step 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 = $\frac{x}{36}$  'x' is the job

Rate S = $\frac{x}{18}$  'x' is the job

So, using the equation of rates

        $Rate total =\frac{x}{36} + \frac{x}{18}$

Rate total is going to be a job in 2 hours so = $\frac{1}{2}$

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

$\frac{1}{2}= x*\frac{3}{36}$  factoring the x

$\frac{1}{2}= x*\frac{1}{12}$  simplifying

x= $\frac{12}{2}$

x= 6