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Two locomotives approach each other on parallel tracks. Each has a speed of v = 95 km/h with respect to the ground. If they are initially d = 7.5 km apart, how long will it be before they reach each other?

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    The speed at which the two objects are approaching each other (from the trains' perspective) is 95 km/h (x 2) = 190 km/h.

    If they are 7.5 km apart at first, you can set up a proportion:

    190 km 7.5 km
    ------ = ---------
    1 hr x hr


    Cross-multiply the terms and set them equal to each other.

    (190 km)(x hr) = (7.5 km)(1 hr)


    Divide both sides by (190 km).

    (190 km)(x hr) = (7.5 km)(1 hr)
    -------------- --------------
    190 km 190 km


    x hr = (7.5 kmh)/190 km

    x hr = 0.03947368421 hr.
    (sig figs = 0.039 hr)



    The unit of hr. may not be very useful in this case, so let's convert hrs to min using dimensional analysis:

    0.03947368 hr 60 min
    ------------- x ------------

    1 1 hr


    = 2.36 minutes
    (sig figs = 2.4 minutes)

    Hope this helps!

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