Ratios/Rates Problem

I don't understand this statement: "We can use the rate of the fastest machine to determine the unknown multiplier: 5x = 0.5 ==> x = 1/10"

On ratio questions, people often like to let the unknown quantities be equal to the know ratio times x

Example: white marbles to red marbles are in ratio 2:3, then let the amounts be 2x and 3x

Here, it is the rates that are given in the ratio, 1:2:3:5
So, we could say: Let the rates be x, 2x, 3x, and 5x
x is a multiplier because it is what we multiply the ratio values (1, 2, 3, 5) by to get the actual rate

So, the fastest has a rate of 0.5 as you said, so 0.5 = 5x, and x = 0.1
Now we can multiply the other ratio values (1, 2, 3) to get the rates for the other machines (.1, .2, .3)

The combined rate of the others is then 0.6, and we use the equation 0.6 * T = 3 to solve.