Let the two rates be x and y.
It was given that the sum of the two rates was $155. This means that:
[tex]x+y=155[/tex]The total charge is $1425. If the two mechanics worked 15 hours and 5 hours respectively at x and y dollars per hour, then it can be had that:
[tex]\begin{gathered} 15x+5y=1425 \\ \therefore \\ 3x+y=285 \end{gathered}[/tex]Subtract the two equations to solve for x:
[tex]\begin{gathered} 3x-x+y-y=285-155 \\ 2x=130 \\ \therefore \\ x=65 \end{gathered}[/tex]Substitute x = 65 into the first equation:
[tex]\begin{gathered} 65+y=155 \\ y=155-65 \\ y=90 \end{gathered}[/tex]Hence, the two rates are $65 per hour and $90 per hour.
The mechanic who worked 15 hours charged $65 per hour.
The mechanic who worked 5 hours charged $90 per hour.