Step 1 :Given that the marble travels 1/4 of the path in 3 1/4 seconds, we can find the time it takes to travel the full path by multiplying the time it takes to travel 1/4 of the path by 4.
Step 2 :Let's denote the time it takes for the marble to travel 1/4 of the path as \(time_{quarter}\) and the time it takes to travel the full path as \(time_{full}\).
Step 3 :We have \(time_{quarter} = 3.25\) seconds.
Step 4 :To find \(time_{full}\), we multiply \(time_{quarter}\) by 4: \(time_{full} = time_{quarter} \times 4\).
Step 5 :Substituting the given value into the equation, we get \(time_{full} = 3.25 \times 4 = 13\) seconds.
Step 6 :Final Answer: The marble takes \(\boxed{13}\) seconds to travel the full length of the path.