A bus traveled on the highway and on local roads to complete a trip of 160   miles . The

Question

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?

A.

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

B.

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

C.

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

D.

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

Accepted Answer

Choice B is correct. If the bus traveled at an average speed of 55 &#160; miles &#160; per &#160; hour &#160; mph 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 &#160; 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 &#160; mph on the highway and 55 &#160; 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 &#160; mph on the highway and 55 &#160; mph on local roads.

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