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9 August, 21:15

A cyclist traveling at 26 mph is followed 6 hours later by a car traveling at 78 mph. How long will it take the car to overtake the cyclist?

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  1. 9 August, 22:09
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    A cyclist traveling at 26 mph is followed 6 hours later by a car traveling at 78 mph.

    Let x be the time taken by the cyclist

    Speed of the cyclist = 26 mph

    WE know distance = speed * time

    so distance traveled by cyclist = 26*x

    car started 6 hours later

    (x-6) is the time taken by the car

    Speed of the car = 78 mph

    distance traveled by car = 78 (x-6)

    when the car overtakes the cyclist then the distance becomes same

    so 26x = 78 (x-6)

    solve for x

    26 x = 78x - 468

    Subtract 78x on both sides

    -52x = - 468

    Divide both sides b y 52

    so x = 9

    Time taken by the cyclist = 9 hours

    car started 6 hours later

    So time taken by the car = 9-6 = 3 hours

    it will take 3 hours for the car to overtake the cyclist
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