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Two cars leave at the same time from points A and B, the distance between them is 280 km. If the cars meet each other, they’ll meet in 2 hours. But if they go in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of both of the cars?

Respuesta :

kanest
Set up the following equations:

[tex]2x + 2y = 280[/tex]

[tex]14x - 14y = 280[/tex]

x represents car A's speed, and y represents car B's speed.

We'll use elimination to solve this system of equations. Multiply the first equation by 7:

[tex](2x + 2y = 280) * 7 = 14x + 14y = 1960[/tex]

[tex]14x - 14y = 280[/tex]

Combine both equations:

[tex]28x = 2240[/tex]

Divide both sides by 28 to get x by itself:

[tex]x = 80[/tex]

The speed of car A is 80 mph.

Since we now know the value of one of the variables, we can plug it into the first equation:

[tex]2(80) + 2y = 280[/tex]

[tex]160 + 2y = 280[/tex]

Subtract 160 from both sides.

[tex]2y = 120[/tex]

Divide both sides by 2 to get y by itself:

[tex]y = 60[/tex]

The speed of car B is 60 mph.

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