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finance Really wants to Beat The GMAT! Default Avatar
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rate problem Post Mon Jul 18, 2011 5:28 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

    A. 1 hour

    B. 1 hour 10 minutes

    C. 2 hours 30 minutes

    D. 1 hour 40 minutes

    E. 2 hours 10 minutes

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    amit2k9 GMAT Destroyer!
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    Post Mon Jul 18, 2011 7:43 am
    t be the time when A and B meet up.
    d be the total distance between the two cities.
    A and B be the individual speeds.

    thus, At+ Bt = d
    also, At+ 2/3* A = d
    and Bt+3/2* B = d

    thus, At+Bt = At+2/3 * A gives Bt = 2/3*A
    and At+Bt = Bt+3/2*B gives At = 3/2 * B

    hence, At = A/t * 2/3 * 3/2 gives t=1.

    thus total time for A is 1hr +40 mins.

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    newgmattest Rising GMAT Star Default Avatar
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    Post Mon Jul 18, 2011 10:15 pm
    Any help on this please?

    finance Really wants to Beat The GMAT! Default Avatar
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    Post Mon Jul 18, 2011 11:42 pm
    amit2k9 wrote:
    also, At+ 2/3* A = d
    and Bt+3/2* B = d

    I didn't get this part. What is 2/3*A?? How did you find 3/2 * B??

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    Post Tue Jul 19, 2011 3:52 am
    finance wrote:
    Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

    A. 1 hour

    B. 1 hour 10 minutes

    C. 2 hours 30 minutes

    D. 1 hour 40 minutes

    E. 2 hours 10 minutes
    We can plug in the answers, which represent the time for A to travel the entire distance.

    We should start with the median amount of time, 1 hour + 40 minutes.

    Answer choice D: Total time for A = 100 minutes.
    Since A travels for 40 minutes after A and B meet, time for A and B to meet = 100-40 = 60 minutes.
    Since B travels for 90 minutes after A and B meet, total time for B = 60+90 = 150 minutes.
    Let distance = 300 miles.
    Rate for A = d/t = 300/100 = 3 miles per minute.
    Rate for B = d/t = 300/150 = 2 miles per minute.
    When elements work together to cover a distance, we add their rates.
    Combined rate for A and B = 3+2 = 5 miles per minute.
    Time for A and B to meet = d/r = 300/5 = 60 minutes. Success!

    The correct answer is D.

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    Post Sat May 19, 2012 12:24 pm
    GMATGuruNY wrote:
    finance wrote:
    Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

    A. 1 hour

    B. 1 hour 10 minutes

    C. 2 hours 30 minutes

    D. 1 hour 40 minutes

    E. 2 hours 10 minutes
    We can plug in the answers, which represent the time for A to travel the entire distance.

    We should start with the median amount of time, 1 hour + 40 minutes.

    Answer choice D: Total time for A = 100 minutes.
    Since A travels for 40 minutes after A and B meet, time for A and B to meet = 100-40 = 60 minutes.
    Since B travels for 90 minutes after A and B meet, total time for B = 60+90 = 150 minutes.
    Let distance = 300 miles.
    Rate for A = d/t = 300/100 = 3 miles per minute.
    Rate for B = d/t = 300/150 = 2 miles per minute.
    When elements work together to cover a distance, we add their rates.
    Combined rate for A and B = 3+2 = 5 miles per minute.
    Time for A and B to meet = d/r = 300/5 = 60 minutes. Success!

    The correct answer is D.
    Hi,

    How can we assume it to be 300?
    Also can someone please explain how the same assumption will not lead us to the result if we choose some other option to deal with in the first place.

    TIA,
    GK

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