We'll use what you came up with to illustrate. Okey-doke?.

Let a=hrs apprentice worked

Let m=hrs master worked.

Let x=apprentice's rate

Let y=master's rate.

System of equations:

ax=90....[1]

my=50....[2]

a+m=8....[3]

y-x=10....[4]

90/x=a

50/y=m

Sub into [3]:

90/x+50/y=8

Sub [4] into [3]:

90/(y-10)+50/y=8

Solve for y=25....The masters hourly rate.

That gives $15 for the apprentice's hourly rate.

The apprentice worked 6 hrs and the master worked 2.

15(6)=90, 25(2)=50