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5 July, 11:54

On a particular day, the wind added 2 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 2 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 45 miles with the wind, he could go only 33 miles against the wind. What is his normal bicycling speed with no wind?

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  1. 5 July, 12:04
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    Let the normal bicycling speed with no wind = x mph

    So, speed with the wind = (x+2) mph

    and speed against the wind = (x-2) mph

    It means

    Time taken in going with the wind = Distance/speed = 45 / (x+2) hours

    and

    Time taken in going against the wind = 33 / (x-2) hours

    And Both times are same, according to the question

    So

    45 / (x+2) = 33 / (x-2)

    On cross multiplying, we get

    45 (x-2) = 33 (x+2)

    45x-90 = 33x+66

    Add 90 to both sides

    45x - 90 + 90 = 33x + 66 + 90

    45x = 33x + 156

    Subtract 33x from both sides

    45x - 33x = 33x - 33x + 156

    12x = 156

    Divide both sides by 12

    x = 13

    That implies

    The normal bicycling speed = 13 Miles per hour
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