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. 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? Choices: (A)1,200 - 500h = 510 - 160h (B)1,200 - 510h = 500 - 160h How many hours will it take for the plane and the helicopter to be the same distance from the airport? Simplify any fractions. ____ hours

Question

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. 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?   Choices: (A)1,200 - 500h = 510 - 160h (B)1,200 - 510h = 500 - 160h  How many hours will it take for the plane and the helicopter to be the same distance from the airport? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set up equations: Set up the equations for the distances of the plane and the helicopter from the airport after h hours. 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: Distance_plane = 1,200 - 510h 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: Distance_helicopter = 500 - 160hDetermine correct equation: Determine the correct equation that equates the distances of the plane and the helicopter from the airport. We want to find the time h when the distances are the same, so we set the two equations equal to each other: 1,200 - 510h = 500 - 160hIdentify correct choice: Identify the correct choice from the given options. Comparing the equation from Step 2 with the choices given: (A) 1,200 - 500h = 510 - 160h (This is incorrect because it does not match the equation we derived.) (B) 1,200 - 510h = 500 - 160h (This is correct because it matches the equation we derived.) 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. 1,200 - 510h = 500 - 160h To solve for h, we first combine like terms by adding 510h to both sides and subtracting 500 from both sides: 1,200 - 500 = 510h - 160h 700 = 350h Now, divide both sides by 350 to solve for h: h = 700 / 350 h = 2

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