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How long does it take an automobile traveling in the left lane of a highway at 70.0 km/h to overtake (become even with) another car that is traveling in the right lane at 20.0 km/h when the cars' front bumpers are initially 110 m apart?
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  • Math -

    let the distance needed to pass be x km
    so the time taken by the slower car = x/20
    and the time taken by the faster car = (x+.110)/70

    but those times are equal, so ....
    x/20 = (x+.110)/70
    70x = 20x + 2.2
    50x = 2.2
    x = 2.2/50 = .044

    time taken by slower car to be overtaken = .044/20
    = .0022 hours
    = 7.92 seconds

    notice .044/20 = .0022
    and (.044 + .110)/70 = .0022

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