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Brenda and Sally run in opposite direction on a circular tra

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Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 03 Oct 2013, 06:28
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Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 03 Oct 2013, 09:20
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fozzzy wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Nice problem. +1.

First time together they run half of the circumference.
Second time together they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 200 + 150 = 350 meters.

Answer: C.
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Oct 2013, 07:33
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avinashrao9 wrote:
Bunuel wrote:
fozzzy wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Nice problem. +1.

First time they run half of the circumference.
Second time they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full cimcufrence) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 200 + 150 = 350 meters.

Answer: C.


Does opposite direction mean running towards each other or running behind each other??
Bunuel, could you please elaborate on the concept of running half the circumference and full circumference..
I am confused :( :( :(


opposite direction means running towards each other ....if they run behind each other then its in same direction.

moreover since starting point is diametrically opposite point and they are running towards each other so the sum of distances travelled by both will be equal to perimeter of semicircle. ==>this is the first meeting point.

now from this point they are running opposite to each other again.
so second time when they will meet ...sum of distance travelled by both will be equal to perimeter of full circle i.e full circumference.

moreover since they have constant speed.
for covering distance equal to semi circle==>brenda contributes 100 m
now since speed is constant so for covering distance 2 times of distance equal to semicircle==>brenda will contribute 2*100 = 200 m

hope its clear
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Re: Brenda and sally run in opposite direction on a circular tra  [#permalink]

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New post 03 Oct 2013, 08:09
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Lets say respective speeds are B and S for Brenda and Sally and distance of the circular track be 2d.

1st case, they run half of the distance of the circular track before meeting since they are running in opposite direction.
so,

dB/(B+S)=100 (Brinda covered 100 m)

2nd case, they run for full circular track and Sally covered 150m.

2dS/(B+S)=150

solve and we will get 3B = 4S

put this in any of the above equation and calculate for 2d = 350.
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Oct 2013, 06:54
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Bunuel wrote:
fozzzy wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Nice problem. +1.

First time they run half of the circumference.
Second time they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full cimcufrence) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 200 + 150 = 350 meters.

Answer: C.


Hi Bunuel,

Why do we assume that Brenda runs for 2*100 = 200 meters for the second part of the problem?
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Oct 2013, 07:14
Bunuel wrote:
fozzzy wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Nice problem. +1.

First time they run half of the circumference.
Second time they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full cimcufrence) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 200 + 150 = 350 meters.

Answer: C.


Does opposite direction mean running towards each other or running behind each other??
Bunuel, could you please elaborate on the concept of running half the circumference and full circumference..
I am confused :( :( :(
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Oct 2013, 07:54
blueseas wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Quote:
moreover since they have constant speed.
for covering distance equal to semi circle==>brenda contributes 100 m
now since speed is constant so for covering distance 2 times of distance equal to semicircle==>brenda will contribute 2*100 = 200 m

hope its clear


Aaahh. If Brenda accounts for 200 meters, then shouldn't Sally cover 150 meters + X meters for the entire track? Thanks!
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Oct 2013, 09:20
pauc wrote:
blueseas wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Quote:
moreover since they have constant speed.
for covering distance equal to semi circle==>brenda contributes 100 m
now since speed is constant so for covering distance 2 times of distance equal to semicircle==>brenda will contribute 2*100 = 200 m

hope its clear


Aaahh. If Brenda accounts for 200 meters, then shouldn't Sally cover 150 meters + X meters for the entire track? Thanks!


No. Second time they rum full circumference and we are told that second time Sally runs 150 meters.
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Oct 2013, 19:47
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fozzzy wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


1. Since they start from diametrically opposite points and they run in opposite directions, the first time they meet they would have together run half the circular track. So when together they run half the track , Brenda covers 100 m
2. Second time they meet , together, they would have covered the full circular track.
3. Brenda would have covered 200 m since she covers 100m m in the first case.
4. It is given, Sally covers 150 m. Total length of the full circular track is 200+150=350m
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 29 Nov 2013, 13:41
Dear Brunel ,

Please explain with some diagram . I got answer but my view point is little different .
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 29 Nov 2013, 14:13
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archit wrote:
Dear Brunel ,

Please explain with some diagram . I got answer but my view point is little different .


The distances covered by Brenda in first and second rounds are in blue and the distances covered by Sally in first and second rounds are in green:
Attachment:
Untitled2.png
Untitled2.png [ 6.02 KiB | Viewed 16468 times ]

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 200 + 150 = 350 meters.

Hope it helps.
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 06 Jul 2014, 14:52
seabhi wrote:
sorry Bunuel, but how are you calculating that Brenda ran 200 m, its not mentioned that they met exactly after the same time, as they met before or double the time.


Since together Brenda and Samuel ran half the circle and in that Brenda ran 100m, When they run the complete circle Brenda will run 2*100= 200 m
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 04 Feb 2019, 00:25
Bunuel wrote:
fozzzy wrote:
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500


Nice problem. +1.

First time together they run half of the circumference.
Second time together they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 200 + 150 = 350 meters.

Answer: C.


Is this implied that the speed of both the girls is same? Would this method work if the speed of both the girls is different.?
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Re: Brenda and Sally run in opposite direction on a circular tra  [#permalink]

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New post 08 Feb 2019, 07:19
I could not understand why the next time they both meet, Brenda would cover 200m. So, I took a different approach:

If t is the time they meet for the first time and d is the distance of semi circular path, then
Brenda's speed = 100/t
Sally's speed = (d-100)/t

Next they both start from same point in opposite directions and meet at some random point on the track.
So, relative speed = 100/t +(d-100)/t = d/t
total track length = 2d
Point of meeting = 2d/d/t = 2t

So, distance covered by Sally:
150 = 2t*(d-100)/t
2d = 350 m

Ref: https://www.hitbullseye.com/Quant/Circular-Motion.php
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Re: Brenda and Sally run in opposite direction on a circular tra   [#permalink] 08 Feb 2019, 07:19
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