A plane and a helicopter are both flying toward Clover City Airport. The plane is $1,200$ miles from the airport, and it is flying at a constant speed of $510$ miles per hour. The helicopter is $500$ miles from the airport, and it is flying at a constant speed of $160$ miles per hour. $\newline$ Which equation can you use to find $h$ , the number of hours it will take for the plane and the helicopter to be the same distance from the airport? $\newline$ Choices: $\newline$ (A) $1,200 - 510h = 500 - 160h$ $\newline$ (B) $1,200 - 500h = 510 - 160h$ $\newline$ How many hours will it take for the plane and the helicopter to be the same distance from the airport? $\newline$ Simplify any fractions. $\newline$ ____ hours $\newline$

Full solution

Q. A plane and a helicopter are both flying toward Clover City Airport. The plane is

1,200

miles from the airport, and it is flying at a constant speed of

510

miles per hour. The helicopter is

500

miles from the airport, and it is flying at a constant speed of

160

miles per hour.

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Which equation can you use to find

h

, the number of hours it will take for the plane and the helicopter to be the same distance from the airport?

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Choices:

\newline

(A)

1,200 - 510h = 500 - 160h

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(B)

1,200 - 500h = 510 - 160h

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How many hours will it take for the plane and the helicopter to be the same distance from the airport?

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Simplify any fractions.

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____ hours

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Understand the problem: Understand the problem. $\newline$ We need to find the time at which the plane and the helicopter will be the same distance from the airport. The plane is $1,200$ miles away and travels at $510$ mph, while the helicopter is $500$ miles away and travels at $160$ mph.
Set up the equation: Set up the equation. $\newline$ The distance each will travel is the product of their speed and time. Since we want to find when they are the same distance from the airport, we set their remaining distances to the airport equal to each other. $\newline$ Remaining distance for the plane: $1,200 - 510h$ $\newline$ Remaining distance for the helicopter: $500 - 160h$ $\newline$ Equation: $1,200 - 510h = 500 - 160h$
Identify the correct equation: Identify the correct equation from the choices. $\newline$ The equation we derived in Step $2$ matches choice (A). $\newline$ Correct equation: (A) $1,200 - 510h = 500 - 160h$
Solve the equation for h: Solve the equation for h. $\newline$ $1,200 - 510h = 500 - 160h$ $\newline$ Add $510h$ to both sides: $1,200 = 500 + 350h$ $\newline$ Subtract $500$ from both sides: $700 = 350h$ $\newline$ Divide both sides by $350$ : $h = \frac{700}{350}$ $\newline$ Calculate h: $h = 2$