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9 April, 08:02

In a certain number of hours a woman traveled 6 km. If she had traveled 3 km more per hour, it would have taken her 7 h less to make the journey. How many kilometers did she travel per hour? (Keep three significant digits.

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  1. 9 April, 08:15
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    We will define the following variables to solve the problem:

    s: normal speed

    t: normal time

    We write the following system of equations:

    6 = s * t

    6 = (s + 3) * (t-7)

    Rewriting the equation two we have:

    6 = s * t - 7s + 3t - 21

    Substituting:

    s = 6 / t

    6 = (6 / t) * t - 7 (6 / t) + 3t - 21

    Multiplying both sides by t:

    6t = 6t - 42 + 3t ^ 2 - 21t

    Rewriting:

    3t ^ 2 - 21t - 42 = 0

    We take the positive root:

    t = 7/2 + root (105) / 2

    t = 8.62 h

    We look for the value of the speed:

    s = 6 / t

    s = 6 / 8.62

    s = 0.696 km / h

    Answer:

    she did travel 0.696 kilometers per hour
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