Driving Your brother and sister took turns driving on a 635-mile trip that took 11 hours to complete. Your brother drove at a constant speed of 60 miles per hour and your sister drove at a constant speed of 55 miles per hour. Let x be the number of miles your brother drove and let y be the number of miles your sister drove. Solve the linear system x + y = 11 and 60x + 55y = 635 to find the number of miles each of your siblings drove. Show your work.

Answer: The brother drove 6 hours and the sister drove 5 hours of the trip

Step-by-step explanation:

Your brother drove 35 miles, and your sister drove 600 miles.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have the following system of equations:

x + y = 11                ....(i)

60x + 55y = 635  ....(ii)

Using the elimination method:

Multiply equation 1 by 55, equation 2 by -1, and add both equations together:

55x + 55y = 605, -60x - 55y = -635

Simplify and solve for x: -5x = -30

x = 6

Substitute this value of x back into equation 1 to find y:

y = 11 - 6 = 5

Thus, your brother drove 35 miles, and your sister drove 635 - 35 = 600 miles.

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