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7 August, 09:29

A man can walk from A to B and back in a certain time at 7 km/hr. If he walks from A to B at 8 km/hr and returns from B to A at 6 km/hr he takes 2 minutes more. Find the distance between A and B.

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  1. 7 August, 11:18
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    We calculate the speed by dividing the distance over time:

    s = d/t

    So the distance described in the problem is always the same, A to B and B to A.

    But we are told that;

    7 = d/t

    7 = 2d / (t + 2)

    that is, the first equation say that at speed 7 km/h a distance d is walked in a time t

    the second equation say that at a average speed of 7 (that is 8 on one way and 6 in the other: 8 + 6 = 14, half of it), twice the distance is walked in a time equal to the first time plus 2 minutes.

    So we have a system of linear equations, 2 of them with two unknowns, we can solve that:

    7 = d/t

    7 = 2d / (t + 2)

    lets simplify them:

    7t = d

    7 (t + 2) = 2d

    7t = 2d - 14

    we substitute the first in the second:

    7t = 2d - 14

    7t = d

    so:

    d = 2d - 14

    d = 14

    so the distance between A and B is 14 km
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