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# Two friends, Tanaya and Stephen were standing together. Tanaya begins

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Manager
Joined: 14 Oct 2014
Posts: 51
Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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Updated on: 07 Apr 2015, 10:44
7
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:51) correct 33% (03:02) wrong based on 117 sessions

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Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Originally posted by manishbhusal on 07 Apr 2015, 10:30.
Last edited by Bunuel on 07 Apr 2015, 10:44, edited 1 time in total.
Renamed the topic and edited the question.
Director
Joined: 07 Aug 2011
Posts: 502
GMAT 1: 630 Q49 V27
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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07 Apr 2015, 12:12
2
3
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Its not that hard as it seems by wording.

Let say tanya walked x miles after stephan started.
$$\frac{X+3}{9}$$ =$$\frac{x}{3}$$
X=1.5 so time taken by stephen = 4.5/9=30mins

Next equation is 2x+6/9= x/3
x=6 so stephen would take 2hr

2hr-30min =90min
##### General Discussion
Manager
Joined: 17 Mar 2015
Posts: 115
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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07 Apr 2015, 14:24
2
t1 - time it takes to cover the same distance tanya covered.
$$3 + t1*3 = 9*t1, t1 = 1/2$$
t2 - time it takes to cover twice of the distance Tanya covered
$$2*(3+t2*3) = 9*t2, t2 = 2$$
$$t2 - t1 = 1.5 = 90$$ minutes, answer C.
Manager
Joined: 14 Oct 2014
Posts: 51
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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07 Apr 2015, 17:59
Lucky2783 wrote:
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Its not that hard as it seems by wording.

Let say tanya walked x miles after stephan started.
$$\frac{X+3}{9}$$ =$$\frac{x}{3}$$
X=1.5 so time taken by stephen = 4.5/9=30mins

Next equation is 2x+6/9= x/3
x=6 so stephen would take 2hr

2hr-30min =90min

Would you mind telling how you got the second equation. I understood the L.H.S part i.e (2x+6) is twice the distance of what tanya had covered.so time taken = (2x+6)/9, but i couldn't understand the R.H.S part of second equation . i.e how we got x/3 and how (2x+6)/9 is equal to x/3.

Thanks
Manish
Director
Joined: 07 Aug 2011
Posts: 502
GMAT 1: 630 Q49 V27
Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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07 Apr 2015, 22:12
1
manishbhusal wrote:
Lucky2783 wrote:
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

I did it like this

Let's assume that by the time Stephen catches up with tanaya she has travelled x miles. In addition she covered 3 miles in 1st hour. Time taken by pooja to travel x miles = time taken by stephen to cover 3+x miles.
so
(3+x)/9=x/3 =>9x=9+3x => 6x=9 => x=3/2 = 1.5 miles. so David travels 4.5 miles to meet tanya. time taken = 4.5/9 = 30 minutes.

time taken to cover twice the distance tanya covered = 9/9= 1 hours. so difference = 60-30 = 30 minutes. But answer is 90 minutes.

PS- I Picked the question from here http://www.veritasprep.com/blog/2011/06 ... se-in-tsd/

Its not that hard as it seems by wording.

Let say tanya walked x miles after stephan started.
$$\frac{X+3}{9}$$ =$$\frac{x}{3}$$
X=1.5 so time taken by stephen = 4.5/9=30mins

Next equation is 2x+6/9= x/3
x=6 so stephen would take 2hr

2hr-30min =90min

Would you mind telling how you got the second equation. I understood the L.H.S part i.e (2x+6) is twice the distance of what tanya had covered.so time taken = (2x+6)/9, but i couldn't understand the R.H.S part of second equation . i.e how we got x/3 and how (2x+6)/9 is equal to x/3.

Thanks
Manish

Hi Manish,

Lets assume that Tanya walked Y Miles when Stephen ran twice the distance she walked.

stephen had to run 2*(Y+3) .

2*(Y+3) /9 = Y/3 (tanya walked only Y Miles when stephen started to run )

hope it is clear .
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Manager
Joined: 19 Mar 2015
Posts: 57
Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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08 Apr 2015, 02:30
3
Assume Tanya travels for t hours.
So, Stephen travels for (t-1) hours

Since distance is the same
3t = 9(t-1)
t = 1.5 hours
So, Stephen travels for 0.5 hours to travel the same distance as Tanya.

Now, Stephen is supposed to travel twice the distance.
Again, suppose Tanya travels for t hours
So, Stephen travels for (t-1) hours
Since Stephen travels twice the distance as Tanya does,
9(t-1) = 2*3t
t = 3 hours
So, Stephen travels for 2 hours to travel twice the distance as Tanya.

So, difference = 2 - 0.5 = 1.5 hours = 90 minutes.
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Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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21 Feb 2016, 11:51
1
manishbhusal wrote:
Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins
(B) 72 mins
(C) 90 mins
(D) 100 mins
(E) 120 mins

oh nice..that's a good brain killer.

after 1 hour, tanya traveled for 3 miles. Stephen 0.
after 2 hours, tanya - 6 miles, stephen -9 miles
after 3 hours, tanya 9 miles, stephen - 18 miles.
ok, so stephen needs 2 hours to cover twice the distance tanya has walked.

now, time needed for stephan to cover the same distance tanya has walked.
1 hour -> tanya 3, stephen -0.
we know the rates of each.
in 20 minutes, tanya walks 1 miles, stephen 3.
so after 1h 20 mins, tanya walked 4 miles. stephen in 20 mins - 3 miles.
so if 20 mins for tanya 1 mile and for stephen 3, then in 10 mins, tanya will walk 0.5 miles and stephen 1.5
so...after another 10 mins, tanya 4.5 miles, stephen 4.5 miles.
we can see that stephen needs 30 mins to cover the same distance that tanya has covered.

now, 30-120=-90. since we are asked for the POSITIVE difference, -90*-1 = 90 mins.
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Joined: 07 Dec 2014
Posts: 1224
Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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21 Feb 2016, 14:03
let t=Stephen's time
t+1=Tanaya's time
equation 1: 9t=3(t+1)
t=1/2 hour=30 minutes
equation 2: 9t=(2)(3)(t+1)
t=2 hours=120 minutes
120-30=90 minutes
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Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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12 Jan 2018, 07:46
I'll be honest this is a really poorly written question and I have to wonder if this was written by a native English speaker because what the question is asking for isn't an answer. The positive difference between the distance she's covered and twice the distance she's covered is going to change based on how long she's walking. We don't know how long she's been walking. This question needs to be rewritten.
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Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins  [#permalink]

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18 May 2019, 11:59
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Re: Two friends, Tanaya and Stephen were standing together. Tanaya begins   [#permalink] 18 May 2019, 11:59
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