Question

Jayden travels 13/18 feet in 9/26 seconds. Find the speed of Jayden in feet per second.
250/81 ft/sec
243/81 ft/sec
169/81 ft/sec
162/81 ft/sec

Answer 1

To find the speed of Jayden in feet per second, we can use the formula:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

Given that Jayden travels \( \frac{13}{18} \) feet in \( \frac{9}{26} \) seconds, we can plug in the values:

\[
\text{Speed} = \frac{\frac{13}{18}}{\frac{9}{26}}
\]

To divide fractions, we multiply by the reciprocal of the denominator:

\[
\text{Speed} = \frac{13}{18} \times \frac{26}{9}
\]

Now, perform the multiplication:

1. **Multiply the numerators**: \( 13 \times 26 = 338 \)
2. **Multiply the denominators**: \( 18 \times 9 = 162 \)

Thus, we get:

\[
\text{Speed} = \frac{338}{162}
\]

Next, we can simplify the fraction. To do that, we'll look for the greatest common divisor (GCD) of 338 and 162.

The GCD of 338 and 162 can be found using the Euclidean algorithm, or by factoring:

- \( 338 = 2 \times 169 \) (where 169 is a prime number)
- \( 162 = 2 \times 81 \) (and 81 is \( 3^4 \))

The GCD is 2, so we divide both the numerator and the denominator by 2:

\[
\frac{338 \div 2}{162 \div 2} = \frac{169}{81}
\]

Thus, the speed of Jayden is:

\[
\text{Speed} = \frac{169}{81} \text{ ft/sec}
\]

Therefore, the correct answer is:

\(\boxed{\frac{169}{81} \text{ ft/sec}}\)