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Math Help - word problem

  1. #1
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    word problem

    a train covered 120 miles at a certian speed. Had the train had been able to travel 10 miles per hour faster, the trip would have been 2 hours shorter. how fast did the train go
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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\frac{{120}}<br />
{{V + 10}} + 2 = \frac{{120}}<br />
{V}<br />


    ...
    Last edited by Peritus; April 2nd 2008 at 04:20 PM.
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  3. #3
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    why are u adding 2 woundt be -2 because the trip would be two hours shorter?
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  4. #4
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    i would be sooo lost lol
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  5. #5
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    I think you're right, should be -2

    because 120/v is the longer time (with the velocity it has)
    120/(v+10) is the shorter time (faster velocity),
    so you need to put -2 to the longer time, in order to equal the shorter time.
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  6. #6
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    ok but i am still lost what do i do next?
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  7. #7
    Len
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    Quote Originally Posted by imbadatmath View Post
    ok but i am still lost what do i do next?
    What Peritus did was use a simple Time=\frac{Distance}{Velocity} forumula

    Distance=D=120 in miles
    Veolicty=V in miles/hours
    Time=T hours

    So for the first train
    T=\frac{120}{V}
    For the second train Velocity is increased by 10 and time is decreased by 2 hours. So
    T-2=\frac{120}{V+10}
    T=\frac{120}{V+10}+2=\frac{120}{V}

    Then just solve for V.
    It will be a quadratic giving you -30 and 20 but -30 is inadmisable because the train would be traveling backwards so your answer is V=20miles per hours
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  8. #8
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    Quote Originally Posted by imbadatmath View Post
    a train covered 120 miles at a certian speed. Had the train had been able to travel 10 miles per hour faster, the trip would have been 2 hours shorter. how fast did the train go
    case 1
    LEt the distance covered = 120

    let x be the speed of the train and let y be the time taken

    Speed=distance/time
    x=120/y

    so xy = 120 ------------------> equation 1

    case 2

    If the train traveled 10 mph faster then time is reduced by 2 hours

    so x+10 = 120/y-2

    (x+10)(y-2) = 120

    multiplying we get

    xy -2x +10y -20 = 120
    from equation 1,

    120 - 2x + 10y - 20 = 120
    subtracting 120 on both sides

    -2x + 10y -20 = 0

    so x = (10y - 20)/2

    x = 5y - 10

    substituting this in equation 1 we get

    (5y-10)y = 120

    5y^2 -10y - 120 = 0

    so now its a quadratic equation, we see that 5 is common on both sides so we divede 5 on both sides

    y^2 -2y - 24 = 0

    factorizing we get

    (y+4)(y-6) = 0

    so either y= -4 or y = 6

    but time can't be negative so we conclude that the time taken is 6 hours, substituting this in equation 1 we get x = 120/6

    x = 20 mph

    so the train was traveling at 20 mph, it's so slow, you can use the bus

    Regards,
    Ice Sync
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  9. #9
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    Quote Originally Posted by imbadatmath View Post
    why are u adding 2 woundt be -2 because the trip would be two hours shorter?
    Look at my answer, you'll be enlightened also read the last sentence of my solution

    Ice Sync
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