Precalculus 11

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It takes an express train 1hr longer to travel 240km than it does for a small plane to travel the same distance. If the plane travels twice as fast as the train, how fast does the plane travel?

This is an ex., they lay out online but I'm confused about how they've laid out the equation.

I would've said:
(1/1)+(240/v)=(240/2v)

They've laid it out with the 1 hr on the other side. If the planes values are on one side & the trains equivalent value (+1hr time) are on the other side why would the 1 be on the side of the plane?

I hope my question makes sense, thanks as always :) <3

  • Precalculus 11 -

    Let n be the speed of the train. Then the planes speed would be 2n. So, you have:
    240/n=(240/2n) +1
    Then, solve for n
    ☺☺☺☺

  • Precalculus 11 -

    but why is the +1 on the planes side of the equation when it was the train that took an hr longer?
    Thanks again :)

  • Precalculus 11 -

    Here is the way I used to explain this concept to my students when I was teaching a "long time ago".

    You did agree that
    the time for the train was greater than the time of the plane by 1, or
    240/n > 240/2n by 1

    right now the left side is greater than the right side by 1
    How do i make them equal ?
    by adding 1 to the smaller side, that is

    240/n = 240/2n + 1

  • Precalculus 11 -

    That makes total sense, thank you very much :)

  • Precalculus 11 -

    Plane takes T hours.
    Train takes T+1 hours.

    Velocity of train = V km/h.
    Velocity of plane = 2V km/h.

    Plane: 2V*T = 240 km.
    Train: V*T = 240 km.

    Therefore, 2V*T = V*(T+1).
    T = 1 h.
    T+1 = 1 + 1 = 2 h.

    2V*T = 240.
    2V * 1 = 240,
    2V = 240 km/h = Velocity of the plane.

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