Eva maintained an average speed of miles per hour for the first hours of her road trip. For the next hours of the trip, she drove at an average speed of . Eva drove a total of miles in hours. Which of the following systems of equations could be used to find how many miles Eva drove in the first hours of the trip?

Question

Eva maintained an average speed of     miles per hour     for the first     hours of her road trip. For the next     hours of the trip, she drove at an average speed of    . Eva drove a total of     miles in     hours. Which of the following systems of equations could be used to find how many miles Eva drove in the first     hours of the trip?

Bytelearn · Accepted Answer

Denote Average Speeds and Times: Let's denote the average speed for the first part of the trip as $ v_1 $ (in miles per hour), the time for the first part as $ t_1 $ (in hours), the average speed for the second part as $ v_2 $, and the time for the second part as $ t_2 $. The total distance is given as $ D $ and the total time as $ T $. We can set up two equations: one for the distance covered in each part of the trip, and one for the total time of the trip.Equation for Distance Covered: The distance Eva drove in the first part of the trip can be represented as $ v_1 \times t_1 $, and the distance in the second part as $ v_2 \times t_2 $. The total distance is the sum of these two distances, so we have the equation $ v_1 \times t_1 + v_2 \times t_2 = D $.Equation for Total Time: The total time of the trip is the sum of the time spent on each part, so we have the equation $ t_1 + t_2 = T $.Solving the System of Equations: Now we have a system of two equations with two variables ($ t_1 $ and $ t_2 $) that can be solved to find the distance Eva drove in the first part of the trip. The system of equations is: 1) $ v_1 \times t_1 + v_2 \times t_2 = D $ 2) $ t_1 + t_2 = T $

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