Is it wise for a firm to employ a worker at $20 per hour when another worker does the same job for $10 per hour?

it would be a rational decision if the first worker was more than twice as productive as the second worker.

it would never be rational to pay a worker that much more than another.

it is illegal to pay a worker that much more than another.
the government will pay firms to give some workers extra pay to increase the total economy.

For me,

It would be a rational decision if the first worker was more than twice as productive as the second worker.

This can happen in real life, for example 2 workers are hired to do the same type of job but one worker graduated with honors, the company can give a higher pay to the worker with honors compared with the other one who graduated. 

It is up to the company on how much they would pay their workers as long as it is above the minimum wage. Though there might be hurt feelings among the workers if they each knew how much they are paid for, it is also better for the company to inform workers that they are paid this certain amount because of the following reasons (graduated w/ honors). 

What do you mean by that?