To find the speed of Jayden, we need to determine how far Jayden travels per unit of time, specifically feet per second. We'll perform this calculation step-by-step.
### Step 1: Express the Distance and Time
Jayden travels a distance of [tex]\( \frac{13}{18} \)[/tex] feet in a time of [tex]\( \frac{9}{26} \)[/tex] seconds.
### Step 2: Calculate the Speed
The speed, [tex]\( S \)[/tex], is given by the formula:
[tex]\[ S = \frac{\text{Distance}}{\text{Time}} \][/tex]
Let's insert the given values into this formula:
[tex]\[ S = \frac{\frac{13}{18}}{\frac{9}{26}} \][/tex]
### Step 3: Simplify the Fraction
To divide by a fraction, we multiply by its reciprocal:
[tex]\[ S = \frac{13}{18} \times \frac{26}{9} \][/tex]
Now, we perform the multiplication:
[tex]\[ S = \frac{13 \times 26}{18 \times 9} \][/tex]
### Step 4: Multiply the Numerators and the Denominators
Calculate the numerator:
[tex]\[ 13 \times 26 = 338 \][/tex]
Calculate the denominator:
[tex]\[ 18 \times 9 = 162 \][/tex]
This gives us:
[tex]\[ S = \frac{338}{162} \][/tex]
### Step 5: Simplify the Fraction
We can simplify the fraction [tex]\( \frac{338}{162} \)[/tex] by finding the greatest common divisor (GCD) of 338 and 162, which is 2. Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{338 \div 2}{162 \div 2} = \frac{169}{81} \][/tex]
Therefore, the speed of Jayden in feet per second is:
[tex]\[ \boxed{\frac{169}{81}} \][/tex]
So, Jayden's speed is [tex]\( \boxed{\frac{169}{81}} \)[/tex] feet per second. This matches one of the given answer choices.
