Step 1 :Let's denote the number of gallons consumed by the first car as \(x\) and the number of gallons consumed by the second car as \(y\).
Step 2 :We can set up the following two equations based on the problem: \(25x + 40y = 1500\) (This equation represents the total distance travelled by the two cars) and \(x + y = 45\) (This equation represents the total gas consumption of the two cars).
Step 3 :Solving this system of equations, we find that \(x = 20\) and \(y = 25\).
Step 4 :This means that the first car consumed 20 gallons of gas and the second car consumed 25 gallons of gas during that week.
Step 5 :Final Answer: The first car consumed \(\boxed{20}\) gallons and the second car consumed \(\boxed{25}\) gallons.