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Math Help - Find the speed

  1. #1
    Raj
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    Find the speed

    Plane A and Plane B flew in opposite directions around the Earth (40,000 km).
    Plane A covered half its distance at a speed of 2,500 km/h and the other half at a speed of 1,000 km/h.
    Plane B spent half its time at 2,500km/h and the other half at 1,000 km/h.
    How long did it take each plane to complete the flight.


    Ok so I found the time of Plane A, half the distance being 20,000 km if i'm correct.
    Therefore Plane A took 28 Hours.

    Problem is i have no idea how to tell how long it took Plane B. Any help please.
    Last edited by Raj; January 31st 2008 at 04:28 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Raj View Post
    Plane A and Plane B flew in opposite directions around the Earth (40,000 km).
    Plane A covered half its distance at a speed of 2,500 km/h and the other half at a speed of 1,000 km/h.
    Plane B spent half its time at 2,500km/h and the other half at 1,000 km/h.
    How long did it take each plane to complete the flight.


    Ok so I found the time of Plane A, half the distance being 20,000 km if i'm correct.
    Therefore Plane A took 28 Hours.

    Problem is i have no idea how to tell how long it took Plane B. Any help please.
    d = vt

    Plain A:
    First half of trip:
    d = 20000 km
    v = 2500 km/h

    So t = \frac{d}{v} = \frac{20000~km}{2500~km/h} = 8~h

    Second half of trip:
    d = 20000 km
    v = 1000 km/h

    So t = \frac{d}{v} = \frac{20000~km}{1000~km/h} = 20~hr

    Thus t = 28 hours, as you say.

    Plain B:

    Let the total trip time be T.

    Then
    t = (1/2)T
    v = 2500 km/h

    d_1 = vt = (2500~km/h) \cdot \left ( \frac{T}{2} \right ) = 1250T

    For the second half of the trip:
    t = (1/2)T
    v = 1000 km/h

    d_2 = vt = (1000~km/h) \cdot \left ( \frac{T}{2} \right ) = 500T

    And we know the total trip distance is d1 + d2 = 40000 km. Thus
    40000 = 1250T + 500T

    Solve for T.

    -Dan
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