As given by the question
There are given that the statement
The first mechanic worked for 20 hours and the second mechanic worked for 5 hours.
Now,
Suppose, the mechanic first-rate is x and the mechanic second rate is y
Then,
The first mechanic works are 20x and the second mechanic works are 5 y
According to question;
Together they charged $1650
So,
The amount of money that earned by both mechanics

Now,
The sum of the two rates was $165 per hour
Then,

That means,

Then,
Put the value of x into the above equation, 20x+5y=1650
So,

Now,
Put the value of y into the equation, x+y=165
So,

Hence, the mechanic first charged is $55 per hour and mechanic second is $110 per hour.