Step 1 :Let's denote: \(x\) = hours Eleanor works at Job A, \(y\) = hours Eleanor works at Job B.
Step 2 :From the problem, we know that Eleanor works a total of 20 hours a week, so we can write the equation: \(x + y = 20\).
Step 3 :We also know that the total amount of money she earns is $134.80, so we can write the equation: \(6.20x + 7.40y = 134.80\).
Step 4 :Solving these two equations, we find that \(x = 11\) and \(y = 9\).
Step 5 :Final Answer: Eleanor worked \(\boxed{11}\) hours at Job A and \(\boxed{9}\) hours at Job B.