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A commercial airplane that is $1500$ miles into a $2500$ mile journey is traveling at $450$ knots in still air when it picks up a tailwind of $150$ knots (in the same direction). If $h$ is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation? $\newline$ $1$ knot = $1.15$ miles per hour

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Convert between Celsius and Fahrenheit

Full solution

Q. A commercial airplane that is

1500

miles into a

2500

mile journey is traveling at

450

knots in still air when it picks up a tailwind of

150

knots (in the same direction). If

h

is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation?

\newline

1

knot =

1.15

miles per hour

Calculate total speed: Calculate the total speed of the airplane with the tailwind. Speed of airplane = $450 \, \text{knots} + 150 \, \text{knots} = 600 \, \text{knots}.$
Convert to mph: Convert the speed from knots to miles per hour. $\newline$ Speed in mph = $600 \text{ knots} \times 1.15 \text{ miles per hour/knot} = 690 \text{ miles per hour}.$
Determine remaining distance: Determine the remaining distance to be traveled. $\newline$ Total journey = $2500$ miles, Distance traveled = $1500$ miles, Remaining distance = $2500$ miles - $1500$ miles = $1000$ miles.
Calculate time remaining: Calculate the time remaining for the journey. $\newline$ Time remaining (h) = Remaining distance / Speed in mph = $1000$ miles / $690$ miles per hour.

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