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Gavin observes a marble travel along a horizontal path at a constant rate. The marble travels $\frac{1}{4}$ of the length of the path in $3 \frac{1}{4}$ seconds. At that rate, how many seconds does it take the object to travel the full length?

On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
To enter a mixed number on the double number line, use a space and the slash key. For example: $31 / 2$

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Final Answer: The marble takes \(\boxed{13}\) seconds to travel the full length of the path.

Steps

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.

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