Mr. Gadgets car broke down on the turnpike. Acme towing charged $30 plus $3 per mile to tow the car. If Mr. Gadgets paid $174, how far was the car towed?

Let's assume that the car was towed for x miles.

The total cost of towing the car is the sum of the flat fee of $30 and the mileage fee of $3 per mile, so it is $30 + $3 * x = $174.

Subtracting $30 from both sides of the equation, we get $3 * x = $174 - $30 = $144.

Dividing both sides of the equation by $3, we find x = $144 / $3 = 48 miles.

Therefore, the car was towed for 48 miles.