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Math Help - Quadratic Equations

  1. #1
    Junior Member
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    Quadratic Equations

    I need help answering this using Quadratic Equations. Please, also explain in detail what you did, so I KNOW how to do it for next time.

    The time required for a train to make a 175 km trip is 1.5 hours less than the time required by bus. The average speed of the bus is 15 km/hr less than that of the train for the same trip. Find the average speed of the train.

    Thanks =)
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  2. #2
    Super Member
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    hi
    let x km/h be the speed of the bus.
    \left(x-15 \right)\left(\frac{175}{x}+1.5 \right) = 175

    \frac{3\,{x}^{2}+305\,x-5250}{2\,x} = 175

    \frac{3\,{x}^{2}-45\,x-5250}{2\,x} = 0

    then x = 50km/h

    and we know that the average speed of the bus is 15 km/hr less than that of the train, hence the average speed of the train is x'=50+15=65km/h
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  3. #3
    Junior Member
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    thank you ^^
    but the answer key which i have been given from my teacher, says that the speed of the train is just 50km/hr.


    :s
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  4. #4
    Super Member
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    Talking

    well,i think 50 km/h is the speed of the bus,but i might be wrong,let me check.
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  5. #5
    Super Member
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    Smile

    sorry about later i was wrong
    let x be the speed of the train and y the speed of the bus,we have :
    x = y + 15
    and
    \left(y+15 \right)\left(\frac{175}{y}-1.5 \right)=175
    -\frac{3\,{y}^{2}+45\,y-5250}{2\,y} = 0
    then y = 35 km/h
    hence x = 50 km/h
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