prep question

jc114 wrote:(1) Machine A can produce x products in 1hour, machine b can produce x products in 3 hours. If machine A and B work together to produce x products, what is the ratio of the products that the faster machine produces to total products?

A. 1/4

B. 1/2

C. 3/4

D.1

E. 5/4

The rate of machine A is x, and the rate of machine B is x/3. Thus, we see that the faster machine is machine A. If the two machines work together for 1 hour, they will make:

x + x/3 = 4x/3

products. Of those 4x/3 products, machine A will have produced x of them. Thus, the ratio of machine A’s product to that of the combined output is:

x/((4x)/3) = 3/4.

Alternate Solution:

Notice that as the two machines operate at constant rates, the ratio of the output of the faster machine (which is machine A) to the total output is the same for any amount time they work together. So, let’s calculate the ratio of the products produced by machine A when the two machines together work for 1 hour.

In one hour, machine A will produce 3x products and machine B will produce x products; for a total of 3x + x = 4x products. Of these 4x products, 3x was produced by machine A; therefore the ratio we are looking for is 3x/4x = 3/4.

Answer: C