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Time,Speed, Distance-Conceptual ; Difficulty: Hard

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Alphonsaj Newbie | Next Rank: 10 Posts Default Avatar
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Time,Speed, Distance-Conceptual ; Difficulty: Hard

Post Mon Jul 18, 2016 2:57 am
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 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.

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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

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Matt@VeritasPrep GMAT Instructor
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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.

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