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Math Help - Four Vehicles

  1. #1
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    Four Vehicles

    A car, a van, a truck and a bike are all travelling tin the same direction on the same road, each at its own onstant speed. At 10 am, the car overtakes the van; at noon, it overtakes the truck; at 2pm it overtakes the bike. At 4 pm the ruck overtakes the bike and, at 6pm, the van overtakes the ruck

    a The speed of the car is 120 km/h and the speed of the truck is 80 km/h
    i Fin the speeds of the van and the bike
    ii Dind the time at which the van overtakes the bike

    b Let c and T represent the speeds, in km/h, of the car and the truck, respectively
    i Find the speeds of the can and the bike in terms of c and T
    ii Show that the time when the van overtakes the bike is the smae, regardless of the speeds of the car and the truck

    any help would be great
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  2. #2
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    I am not doing the entire problem, I just do part of it.

    At 10:00 AM the Van and Car are that the same place. After 2 hours the Car catches up to the Truck. Now, before those two hours the Truck was some distance ahead of the car/van call that s. Thus, the distance the car traveled in those two hours is the distance the trucked traveled plus s. Thus,
    s+2V_{\mbox{truck}}=2V_{\mbox{car}}
    But we know what the speeds are thus,
    s+2(80)=2(120)
    Thus, s=80 \mbox{km}
    That means the distance from the car/van at 10:00 to the truck was 80 kilometers.
    The problem says that at 6pm (after 8 hours) the van overtakes the truck. That means, the the distance the van traveled from 10:00AM to 6:00PM is the same as the distance the truck traveled plus the distance is was already ahead-which we found to be 80.
    Thus,
    8V_{\mbox{van}}=80+8V_{\mbox{truck}}
    Since we know the speed of the truck (divide by eight),
    V_{\mbox{van}}=10+80=90\frac{\mbox{km}}{\mbox{hour  }}
    Thus, the speed of the van is 90 kilometers per hour.
    Last edited by CaptainBlack; June 10th 2006 at 10:27 PM.
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