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Math Help - average speed.

  1. #1
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    average speed.

    “if a cyclist travels at an average speed of 3m/s-1 and turns home at an average speed of 9m/s-1 than what is the average speed of the whole journey?”

    using the equation speed= distance/time
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  2. #2
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    Hello, hana_102!

    This is a classic Trick Question . . .


    If a cyclist travels at an average speed of 3m/s
    and turns home at an average speed of 9m/s,
    what is the average speed of the whole journey?
    \text{Average Speed} \:= \:\frac{\text{Total distance}}{\text{Total Time}}


    We will use: . Time\;=\;\frac{Distance}{Speed}

    Suppose the distance (one way) is d meters.

    He cycled d meters at 3 m/s.
    . . This took him: . \frac{d}{3} seconds.

    He cycled back d meters at 9 m/s.
    . . This took him: . \frac{d}{9} seconds.

    The entire trip took: . \frac{d}{3} + \frac{d}{9} \:=\:\frac{4}{9}d seconds (Total time).

    The total distance is: . 2d meters.


    Therefore, his average speed was: . \frac{2d}{\frac{4}{9}d} \;=\;4.5\text{ m/s}

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  3. #3
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    Thanks for explaining, I understand how you got your answer, but what I don’t get is how you got 4/9 ?
    Sorry if this seems silly. But how does d/3 + d/9= 4/9d?

    Thank you
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  4. #4
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    Hello, hana_102!

    Don't kick yourself too hard . . .

    . . \frac{1}{3} + \frac{1}{9} \;=\;\frac{3}{9} + \frac{1}{9} \;=\;\frac{4}{9}

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  5. #5
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    Thank you. That seems so simple now that I look at it all worked out!!!!!!!!
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