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Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?

How do I put this into two equation and use the matrix to solve it?

  • math -

    u = 2d
    or
    u - 2d = 0
    u + d = 5

    so the matrix would be

    1 -2 0
    1 1 5

    add -1 times the 1st row to the 2nd row. Then you get

    1 -2 0
    0 3 5

    multiply the 2nd row by 1/3:

    1 -2 0
    0 1 5/3

    The 2nd row tells us that d = 5/3, so u = 10/3

  • math -

    I don't know about the matrix, but it is not necessary to solve the problem.

    x = time traveling down river
    2x = time traveling up river.

    x + 2x = 5

    3x = 5

    x = 5/3 hour = 1 hour, 40 minutes

    2x = ?

    I hope this helps.

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