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Algebra / Systems of two linear equations in two variables Difficulty: Medium

A bus traveled on the highway and on local roads to complete a trip of $160 miles$ . The trip took $4 hours$ . The bus traveled at an average speed of $55 miles per hour left parenthesis mph right parenthesis$ on the highway and an average speed of $25 mph$ on local roads. If $x$ is the time, in hours, the bus traveled on the highway and $y$ is the time, in hours, it traveled on local roads, which system of equations represents this situation?

$55 x + 25 y = 4$
$x + y = 160$

$55 x + 25 y = 160$
$x + y = 4$

$25 x + 55 y = 4$
$x + y = 160$

$25 x + 55 y = 160$
$x + y = 4$

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Explanation

Choice B is correct. If the bus traveled at an average speed of $55 miles per hour left parenthesis mph right parenthesis$ on the highway for $x$ hours, then the bus traveled $55 x$ miles on the highway. If the bus traveled at an average speed of $25 mph$ on local roads for $y$ hours, then the bus traveled $25 y$ miles on local roads. It's given that the trip was $160$ miles. This can be represented by the equation $55 x + 25 y = 160$ . It's also given that the trip took $4$ hours. This can be represented by the equation $x + y = 4$ . Therefore, the system consisting of the equations $55 x + 25 y = 160$ and $x + y = 4$ represents this situation.

Choice A is incorrect. This system of equations represents a situation where the trip was $4$ miles and took $160$ hours.

Choice C is incorrect. This system of equations represents a situation where the trip was $4$ miles and took $160$ hours, and the bus traveled at an average speed of $25 mph$ on the highway and $55 mph$ on local roads.

Choice D is incorrect. This system of equations represents a situation where the bus traveled at an average speed of $25 mph$ on the highway and $55 mph$ on local roads.