SOLUTION: Jan and Brian drove a total of 413 miles in 8.8 hours. Jan drove the first part of the trip and averaged 55 miles per hour. Brian drove the remainder of the trip and averaged 45 mi

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Question 1059893: Jan and Brian drove a total of 413 miles in 8.8 hours. Jan drove the first part of the trip and averaged 55 miles per hour. Brian drove the remainder of the trip and averaged 45 miles per hour. For what length of the time did Jan drive?
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Jan and Brian drove a total of 413 miles in 8.8 hours. Jan drove the first part of the trip and averaged 55 miles per hour.
Brian drove the remainder of the trip and averaged 45 miles per hour. For what length of the time did Jan drive?
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Let x and y represent the amount of time Jan drove and Brian drove, respectively.

Then you have the system of two equations

  x +   y = 8.8     (1)   (time equation)
55x + 45y = 413.    (2)   (the distance equation)

To solve it, express x = 8.8-y from (1) and then substitute it into (2) replacing x. You will get

55(8.8-y) + 45y = 413.

Simplify and solve for y.

Then find x.