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A commercial airplane that is $1,500$ miles into a $2,500$ -mile journey is traveling at $450$ knots in still air when it picks up a tailwind of $150$ knots (in the same direction). If $\newline$ $h$ 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 (mph) $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $1,500 + 690h = 2,500$ $\newline$ (B) $\newline$ $1,500 + 600h = 2,500$ $\newline$ (C) $\newline$ $1,500 - 600h = 2,500$ $\newline$ (D) $\newline$ $2,500$ $0$

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Math Problems

Grade 8

Solve equations with variables on both sides: word problems

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Q. A commercial airplane that is

1,500

miles into a

2,500

-mile journey is traveling at

450

knots in still air when it picks up a tailwind of

150

knots (in the same direction). If

\newline

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 (mph)

\newline

Choose

1

answer:

\newline

(A)

\newline

1,500 + 690h = 2,500

\newline

(B)

\newline

1,500 + 600h = 2,500

\newline

(C)

\newline

1,500 - 600h = 2,500

\newline

(D)

\newline

2,500

0

Convert Speed to mph: Convert the airplane's speed from knots to miles per hour (mph). The airplane is traveling at $450$ knots in still air, and it picks up a tailwind of $150$ knots. We need to add these two speeds together and then convert the sum to mph. $450$ knots $+$ $150$ knots $=$ $600$ knots. Now, convert knots to mph using the given conversion rate: $1$ knot $=$ $1.15$ mph. $600$ knots $150$ $1$ $1.15$ mph/knot $=$ $150$ $4$ mph.
Set Remaining Distance Equation: Set up the equation to represent the remaining distance to be covered. $\newline$ The airplane has already covered $1,500$ miles of its $2,500$ -mile journey. The remaining distance is $2,500$ miles - $1,500$ miles = $1,000$ miles. $\newline$ The airplane is now traveling at a speed of $690$ mph due to the tailwind. $\newline$ Let $h$ be the number of hours remaining for the flight. The distance covered in $h$ hours at $690$ mph is $690 \times h$ miles.
Write Total Distance Equation: Write the equation using the remaining distance and the distance that will be covered in $h$ hours. $\newline$ The total distance covered by the end of the flight will be the distance already covered ( $1,500$ miles) plus the distance covered in the remaining hours ( $690 \times h$ miles). $\newline$ So, the equation is $1,500$ miles + $690 \times h$ miles = $2,500$ miles.
Check Answer Choices: Check the answer choices to see which one matches the equation we have derived. $\newline$ The correct equation is $1,500 + 690 \times h = 2,500$ , which matches answer choice (A).