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help me find the distance between cities?

50mph traveling from Denver to Minneapolis, returning by a different route that covered the same number of miles, average was 55 mph what is the distance between two cities if the total traveling time was 32 hours?

5 Answers

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  • 1 decade ago
    Favorite Answer

    so , distance = rate*time

    so, setting up two equations. One for the traveling from Denver to Minneapolis, and one for the traveling from Minneapolis to Denver, you get:

    D1 = R1 * T1

    D2 = R2 * T2

    but you're told that D1=D2 so, just use D instead of D1 and D2 to get:

    D = R1 * T1

    D = R2 * T2

    the rates are given, so you know R1 = 50 and R2 = 55 so you get:

    D = 50T1

    D = 55T2

    and you're also told that T1+T2 = 32 so you now have three equations in three unknowns:

    D = 50T1

    D = 55T2

    T1+T2 = 32

    so rewrite as:

    50T1 + 0T2 - D = 0

    0T1 + 55T2 - D = 0

    1T1 + 1T2 + 0D = 32

    set up a matrix:

    [50 0 -1 | 0]

    [0 55 -1 | 0]

    [1 1 0 | 32]

    swtich the bottom and top to get

    [1 1 0 | 32]

    [0 55 -1 | 0]

    [50 0 -1 | 0]

    now multiply the top by -50 and add those resutls to bottom to get the new bottom matrix of:

    [1 1 0 | 32]

    [0 55 -1 | 0]

    [0 -50 -1 | -1600]

    multiply the bottom by -1 to get rid of negative signs

    [1 1 0 | 32]

    [0 55 -1 | 0]

    [0 50 1 | 1600]

    now divide the middle by 55 to get

    [1 1 0 | 32]

    [0 1 -1/55 | 0]

    [0 50 1 | 1600]

    now multiply the middle by -1 and add to top to get

    [1 0 1/55 | 32]

    [0 1 -1/55 | 0]

    [0 50 1 | 1600]

    now multiply the middle by -50 and add to bottom:

    [1 0 1/55 | 32]

    [0 1 -1/55 | 0]

    [0 0 21/11 | 1600]

    now multiply bottom by 11/21 to get

    [1 0 1/55 | 32]

    [0 1 -1/55 | 0]

    [0 0 1 | 800]

    so the bottom line now shows you that the distance is 800 miles.

  • Anonymous
    1 decade ago

    distance = speed x time for each leg.

    d = 55t1 and d = 50t2

    t1 + t2 = 32

    So d/55 + d/50 = 32

    105d = 32 x 50 x 55 = 88000

    d = 838 miles, approx

  • 1 decade ago

    50+55/2*32/2=840miles distance from cities...i think

  • A
    Lv 4
    1 decade ago

    distance = rate * time

    2d = 55mph * 32 = 1760 miles

    distance = 1760/2 = 880 miles

  • 6 years ago

    hillsdale kansas and peculiar missouri

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