Lets make the rate of the first mechanic be x.
Lets make the rate of the second mechanic be y.
Given that the sum of the two rates of x and y is $215 per hour we can set up two equations.
x + y = 215
y = 215 - x
The cost of the first mechanic is 10x and the cost of the second mechanic is 5y and it's given that the total cost for both is $1600. So we can set up another equation with this given information.
10x + 5y = 1600
Now plug in our value for y into the equation we just made.
10x + 5(215-x) = 1600
10x + 1075 - 5x = 1600
5x + 1075 = 1600
5x = 525
x = 105
Now plug in what we got as x into the equation that we made with y = 215 - x.
y = 215 - 105
y = 110
The first mechanic's rate charged per hour is $105/hr and the second mechanic's rate charged per hour is $110/hr.