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Time,Speed, Distance-Conceptual ; Difficulty: Hard

This topic has 2 expert replies and 1 member reply
Alphonsaj Newbie | Next Rank: 10 Posts Default Avatar
Joined
14 Jul 2016
Posted:
8 messages

Time,Speed, Distance-Conceptual ; Difficulty: Hard

Post Mon Jul 18, 2016 2:57 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Steve & Bill leave points A and B respectively at the same time and travel towards each other on the same road. They meet at point C, between A and B and proceed towards their respective destinations. After meeting Bill, Steve takes 16 minutes more to reach his destination. After meeting Steve, Bill takes 9 minutes more to reach his destination.
    How long did Steve take to travel from A to B, if they did not spend any time at point C?

    A) 25 mins
    B) 23 mins
    C) 28 mins
    D) 144 mins
    E) Cannot be determined with the given data.

    Correct Answer: C

    Source: 4Gmat

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    Post Mon Jul 18, 2016 4:13 am
    Alphonsaj wrote:
    Steve & Bill leave points A and B respectively at the same time and travel towards each other on the same road. They meet at point C, between A and B and proceed towards their respective destinations. After meeting Bill, Steve takes 16 minutes more to reach his destination. After meeting Steve, Bill takes 9 minutes more to reach his destination.
    How long did Steve take to travel from A to B, if they did not spend any time at point C?

    A) 25 mins
    B) 23 mins
    C) 28 mins
    D) 144 mins
    E) Cannot be determined with the given data.
    Let t = the time for Steve and Bill to meet.
    Let the distance = 1 mile.

    Combined rate for Steve and Bill:
    Since Steve and Bill together take t minutes to cover the 1 mile between them, the combined rate for Steve and Bill = 1/t.

    Steve's rate:
    Since Steve takes 16 more minutes after Steve and Bill meet, Steve's time to travel the entire 1 mile = t+16.
    Thus, Steve's rate = 1/(t+16).

    Bill's rate:
    Since Bill takes 9 more minutes after Steve and Bill meet, Bill's time to travel the entire 1 mile = t+9.
    Thus, Bill's rate = 1/(t+9).

    Since the sum of Steve's rate and Bill's rate must be equal to their combined rate, we get:
    1/(t+16) + 1/(t+9) = 1/t

    [(t+9) + (t+16)] / [(t+9)(t+16)] = 1/t

    (2t + 25)/(t² + 25t + 144) = 1/t

    2t² + 25t = t² + 25t + 144

    t² = 144

    t = 12.

    Thus, Steve's time to travel the entire 1 mile = t+16 = 12+16 = 28 minutes.

    The correct answer is C.

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    Thanked by: Alphonsaj
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    Post Mon Jul 18, 2016 5:39 am
    (1) Steve's Rate: Ds/T = Db/16 > Ds and Db are Steve's and Bill's distance traveled upon meeting at C after Time T and equality reflects rate is the same after passing C

    (2) Bill's Rate: Db/T = Ds/9

    From (1) Ds/Db = T/16

    From (2) Ds/Db = 9/T

    Equating the two reflects T^2 = 144 > T = 12> Time to meet at C

    Steve traveled for 16 more minutes, so total time is 12 + 16 = 28

    GMAT/MBA Expert

    Post Wed Jul 20, 2016 10:46 pm
    Let's say the total distance = m miles and that it takes t minutes for the men to meet at point C.

    We know that Steve travels the m miles in (16 + t) minutes, so Steve's rate = m/(16 + t).

    We know that Bill travels the m miles in (9 + t) minutes, so Bill's rate = m/(9 + t).

    We know that when the two men meet, Bill has traveled m/(9 + t) * t miles. We know that it will take Steve 16 minutes to travel that distance after the meeting, so

    16 * Steve's Rate = m/(9+t) * t

    16 * m/(16 + t) = m/(9+t) * t

    16/(16 + t) = t/(9 + t)

    16*(9 + t) = t*(16 + t)

    0 = t² - 144

    0 = (t + 12) * (t - 12)

    We can only have a positive solution, so t = 12. Steve's total time = 16 + t, or 16 + 12, so C.

    Thanked by: Alphonsaj
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