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) $1,200 - 500h = 510 - 160h$ $\newline$ (B) $1,200 - 510h = 500 - 160h$ $\newline$ 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 $\newline$

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Solve equations with variables on both sides: word problems

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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.

\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 - 500h = 510 - 160h

\newline

(B)

1,200 - 510h = 500 - 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

Set up equations: Set up the equations for the distances of the plane and the helicopter from the airport after $h$ hours. $\newline$ The plane's distance from the airport after $h$ hours is $1,200$ miles minus the distance it travels, which is $510$ miles per hour times $h$ hours. So, the equation for the plane's distance is: $\newline$ $\text{Distance}_{\text{plane}} = 1,200 - 510h$ $\newline$ The helicopter's distance from the airport after $h$ hours is $500$ miles minus the distance it travels, which is $160$ miles per hour times $h$ hours. So, the equation for the helicopter's distance is: $\newline$ $h$ $0$
Determine correct equation: Determine the correct equation that equates the distances of the plane and the helicopter from the airport. $\newline$ We want to find the time $h$ when the distances are the same, so we set the two equations equal to each other: $\newline$ $1,200 - 510h = 500 - 160h$
Identify correct choice: Identify the correct choice from the given options. $\newline$ Comparing the equation from Step $2$ with the choices given: $\newline$ (A) $1,200 - 500h = 510 - 160h$ (This is incorrect because it does not match the equation we derived.) $\newline$ (B) $1,200 - 510h = 500 - 160h$ (This is correct because it matches the equation we derived.) $\newline$ Therefore, the correct choice is (B).
Solve for h: Solve the equation for h to find the number of hours it will take for the plane and the helicopter to be the same distance from the airport. $\newline$ $1,200 - 510h = 500 - 160h$ $\newline$ To solve for h, we first combine like terms by adding $510h$ to both sides and subtracting $500$ from both sides: $\newline$ $1,200 - 500 = 510h - 160h$ $\newline$ $700 = 350h$ $\newline$ Now, divide both sides by $350$ to solve for h: $\newline$ $h = \frac{700}{350}$ $\newline$ $h = 2$