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Math Help - speed, distance calculations

  1. #1
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    speed, distance calculations

    A traffic helicopter is flying with an average speed of 144 km/h over a traffic jam on
    the motorway. It takes 7.5 minutes flying in the direction of traffic and 6.5 minutes in
    the opposite direction. What is the length of the traffic jam and the average velocity
    at which the cars move?

    so relative velocity = distance/60 km/s

    518400-velocity of cars =distance/60 km/s
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  2. #2
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    Quote Originally Posted by Duke View Post
    A traffic helicopter is flying with an average speed of 144 km/h over a traffic jam on
    the motorway. It takes 7.5 minutes flying in the direction of traffic and 6.5 minutes in
    the opposite direction. What is the length of the traffic jam and the average velocity
    at which the cars move?

    so relative velocity = distance/60 km/s

    518400-velocity of cars =distance/60 km/s
    I am unsure how how you got the above answers. You should have a system of equations and be careful about the mixed units.

    You should let d be the length of the traffic jam and v be the speed of traffic

    d=\left(\frac{12}{5}-v \right)\left( \frac{15}{2}\right) \quad d=\left(\frac{12}{5}+v \right)\left( \frac{13}{2}\right)
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    How did you obtain those equations?
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    Quote Originally Posted by Duke View Post
    How did you obtain those equations?
    distance equals rate times time

    d=rt
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  5. #5
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    If you were trying to get the speed of the heli into km/minute should you not have multiplied by 60. And I think you have the signs muddled
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    Quote Originally Posted by Duke View Post
    If you were trying to get the speed of the heli into km/minute should you not have multiplied by 60. And I think you have the signs muddled
    ummm no

    144 \frac{\text{km}}{\text{hr}}\cdot \frac{1 \text{hr}}{60 \text{min}}=\frac{12 \text{km}}{5\text{min}}

    Please explain why you think they are wrong and what is your solution?

    I can't really help you if you don't show your work.
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  7. #7
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    Yes you're correct, sorry. I don't understand about rate. Why is it it -v in the equation (12/5-v)*15/2 =d but +v in the other.
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    Quote Originally Posted by Duke View Post
    Yes you're correct, sorry. I don't understand about rate. Why is it it -v in the equation (12/5-v)*15/2 =d but +v in the other.
    When the helicopter is moving the same direction as the traffic its speed relative to the traffic is helicopter minus traffic speed. When it is moving in the opposite direction as traffic its speed relative to the traffic is helicopter plus traffic. A similar but easier to visualize situation is a boat moving on a river. When it goes against the current you subtract the rivers speed, but when it moves with the current you add their velocities.
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