Mixture problem using a system of linear equations

Question

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours Together they charged a total of $2250. What was the rate charged per hour by each mechanic if the sum of the two rates was $1.35 per hour?

Answer 1

20F + 15S = 2250

F+S = 1.35

F= 135-S

20(135-S) + 15S = 2250

2700 - 20S +15S = 2250

5S = 450

S = $90 per hour for the 2nd mechanic

F = $45 per hour for the 1st mechanic

20(45) + 15(90) = 900 +1350 = 2250

there must be a typo in the problem. Either $1.35 was $135

or $2250 was $22.50

Given minimum wages laws, it's likely the sum of wage rates was $135