Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
margarita is driving at the speed of \\(\frac{s - 4}{s^2 - 9s + 20}\\) miles per hour.

the distance margarita covers in \\(\frac{s - 5}{4}\\) hours is \\(\square\\) miles.
express your answer as a fraction in simplest form.

Explanation:

Step1: Recall the distance formula

The formula for distance \( d \) is \( d=\text{speed}\times\text{time} \). Here, speed is \( \frac{s - 4}{s^{2}-9s + 20} \) and time is \( \frac{s - 5}{4} \). So we need to multiply these two expressions: \( d=\frac{s - 4}{s^{2}-9s + 20}\times\frac{s - 5}{4} \).

Step2: Factor the denominator of the speed

Factor \( s^{2}-9s + 20 \). We need two numbers that multiply to 20 and add to - 9. Those numbers are - 4 and - 5. So \( s^{2}-9s + 20=(s - 4)(s - 5) \).

Step3: Substitute the factored form into the distance formula

Substitute \( (s - 4)(s - 5) \) for \( s^{2}-9s + 20 \) in the speed's denominator: \( d=\frac{s - 4}{(s - 4)(s - 5)}\times\frac{s - 5}{4} \).

Step4: Cancel out common factors

We can cancel out \( (s - 4) \) from the numerator and denominator of the first fraction, and we can also cancel out \( (s - 5) \) from the numerator of the second fraction and the denominator of the first fraction. After canceling, we have \( d=\frac{1}{4} \).

Answer:

\(\frac{1}{4}\)