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Math Help - help me out to find the distance

  1. #1
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    help me out to find the distance

    if a man walks at the rate of 5kmph,he misses a train by only 7 min.however if he walks at the rate of 6kmph he reaches the station 5 minutes before the arrival of train.find the distance covered by him to reach the station?
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  2. #2
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    Quote Originally Posted by hena View Post
    if a man walks at the rate of 5kmph,he misses a train by only 7 min.however if he walks at the rate of 6kmph he reaches the station 5 minutes before the arrival of train.find the distance covered by him to reach the station?
    Let d be the distance travelled to the train in kilometres.

    Let s be the speed travelled to reach the train on time in km/h.

    Let t be the time taken to reach the train on time, in hours.

    d = st

    d = 5(t+7/60)

    d = 6(t-5/60)

    5(t+7/60) = 6(t-5/60)

    5t + 35/60 = 6t - 30/60

    t = 65/60

    d = 5(72/60) = 360/60 = 6 kilometres.
    Last edited by sean.1986; May 23rd 2008 at 09:29 PM.
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  3. #3
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    Hello, hena!

    Nice job, Sean!
    . . I have a slightly difference approach . . .


    If a man walks at the rate of 5 km/hr, he misses a train by only 7 minutes.
    However, if he walks at the rate of 6 km/hr, he reaches the station 5 minutes early.
    Find the distance covered by him to reach the station?

    Let d = distance to the station.
    Let T = exact time to reach the station on time.

    We will use: . \text{(Distance)} \;=\;\text{(Speed)} \times\text{(Time)} \quad\Rightarrow\quad t \:=\:\frac{D}{S}


    At 5 km/hr, it takes him: . \frac{d}{5} hours.
    . . But he will be 7 minutes late: . \frac{d}{5} \:=\:T + \frac{7}{60}\;\;{\color{blue}[1]}

    At 6 km/hr, it takes him: . \frac{d}{6} hours.
    . . But he will be 5 minutes early: . \frac{d}{6} \:=\:T - \frac{5}{60}\;\;{\color{blue}[2]}

    Solve the system of equations.

    Subtract [2] from [1]: . \frac{d}{5} - \frac{d}{6} \;=\;\frac{7}{60} + \frac{5}{60} \quad\Rightarrow\quad \frac{d}{30} \:=\:\frac{1}{5}\quad\Rightarrow\quad \boxed{d \:=\:6}

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