Sure, let's walk through the problem step-by-step.
You are given the relationship between distance [tex]\(d\)[/tex] traveled and time [tex]\(t\)[/tex] in hours as [tex]\(t = \frac{1}{500} d\)[/tex]. This means for every mile traveled, it takes [tex]\(\frac{1}{500}\)[/tex] hours.
Let's find out how long it will take for the airplane to travel 800 miles.
1. Identify Known Values:
- Distance traveled, [tex]\(d = 800\)[/tex] miles.
2. Substitute the Known Value into the Equation:
Since the relationship between time and distance is given by [tex]\(t = \frac{1}{500} d\)[/tex], we substitute 800 for [tex]\(d\)[/tex]:
[tex]\[
t = \frac{1}{500} \times 800
\][/tex]
3. Simplify the Expression:
Multiply the fraction by the distance:
[tex]\[
t = \frac{800}{500}
\][/tex]
4. Calculate the Time:
Simplify the fraction:
[tex]\[
t = 1.6 \text{ hours}
\][/tex]
Therefore, it will take the airplane 1.6 hours to travel 800 miles.
