6. Let me first show the graphical solution:
Algebraically: Let P=pay and t=time in hours so P=10t (this equation uses a rate relationship so it’s not y=mx+b). Now, I attached to this a P=7t line but it is translated up an unknown number of units, say P1. P1=10(t1) where t1 is the number of $10/hr hrs worked.
Thus, total P after the $7/hr line is: P=7t+10(t1) where t picks up after the first t1. The $7/hr line goes for 7-(t1) hrs and finishes at a pay of $58 so 58=7(7-(t1))+10(t1) giving 9=3(t1) or t1=3hrs. The rest follows easily from this.