Let the time she drove at 70MPH and 50MPH be x and y respectively.
x is one hour greater than y, so we have: x=y+1··· (1)
The distances she drove at 70MPH and 50 MPH are 70x and 50y respectively, and the difference between them is 100 miles. So, we have: 70x-50y=100
Divide both sides by 10. We have: 7x-5y=10 ··· (2)
Solve the equations for y substituting (1) into (2). We have: 7(y+1)-5y=10
Remove the brackets and simplify the equation, getting 2y=3, so y=1.5 (hours)
Plug y=1.5 into (1). We have: x=1.5+1=2.5 (hours)
CK: Plug x=2.5 and y=1.5 into the left side of (2): 7(2.5)-5(1.5)=10, so LHS=RHS CKD.
The answer: She drove 2.5 hours at 70MPH, then 1.5 hours at 50 MPH.