Jayden travels [tex]\(\frac{13}{18}\)[/tex] feet in [tex]\(\frac{9}{26}\)[/tex] seconds. Find the speed of Jayden in feet per second.

A. [tex]\(\frac{250}{81}\)[/tex] ft/sec
B. [tex]\(\frac{203}{81}\)[/tex] ft/sec
C. [tex]\(\frac{169}{81}\)[/tex] ft/sec
D. [tex]\(\frac{162}{81}\)[/tex] ft/sec



Answer :

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.