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On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, [tex]d[/tex], to the number of hours flying, [tex]t[/tex], is [tex]t = \frac{1}{500} d[/tex].

How long will it take the airplane to travel 800 miles?

Each table represents a proportional relationship. For each, find the constant of proportionality.



Answer :

GinnyAnswer
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.

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