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# The figure below represents a track with identical semi-circular ends

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Math Expert
Joined: 02 Sep 2009
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The figure below represents a track with identical semi-circular ends  [#permalink]

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06 Oct 2014, 07:47
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72
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Difficulty:

85% (hard)

Question Stats:

58% (03:05) correct 42% (03:32) wrong based on 364 sessions

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Tough and Tricky questions: Distance/Rate .

The figure below represents a track with identical semi-circular ends used for a 4-lap relay race involving two 4-person teams (where each team member runs one complete lap around the track). The table below shows the lap times for each runner on Team A and Team B. Assuming that each runner runs at a constant rate, Team A win the race by how many meters?

A. 40 meters

B. $$(40 + 10\pi)$$ meters

C. $$(40 + 20\pi)$$ meters

D. $$(20 + 10\pi)$$ meters

E. $$(20 + 20\pi)$$ meters

Attachment:

Untitled.png [ 26.39 KiB | Viewed 23458 times ]

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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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10 Oct 2014, 21:01
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12
$$Perimeter = 120 + 120 + 30\pi + 30\pi = 240 + 60\pi$$

Refer the modified diagram below:

Attachment:

Untitled.png [ 33.11 KiB | Viewed 20158 times ]

At 178 seconds, when Team A completed the race, last runner of Team B had 42-35 = 7 seconds to complete the race.

We require to find the distance covered in last 7 seconds

Distance covered in 42 seconds is $$240 + 60\pi$$, so distance covered in 7 seconds

$$= \frac{7}{42} * (240 + 60\pi) = 40 + 10\pi$$

##### General Discussion
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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06 Oct 2014, 11:01
11
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Bunuel wrote:

Tough and Tricky questions: Distance/Rate .

The figure below represents a track with identical semi-circular ends used for a 4-lap relay race involving two 4-person teams (where each team member runs one complete lap around the track). The table below shows the lap times for each runner on Team A and Team B. Assuming that each runner runs at a constant rate, Team A win the race by how many meters?

A. 40 meters

B. $$(40 + 10\pi)$$ meters

C. $$(40 + 20\pi)$$ meters

D. $$(20 + 10\pi)$$ meters

E. $$(20 + 20\pi)$$ meters

Attachment:
Untitled.png

radius of the curved part (semi-circle) = 1/2(60) =30
thus perimeter of the track (120*2) + 2pi(30) = 240 + 60pi

now as per the chart, team A beats team b by 7 sec. obviously, the final lap is run by the last runner of team B which takes 42 seconds to run the complete track.

during these 7 secs, this last runner would have covered 7/42 = 1/6 of the lap.

thus Team A defeated team B by 1/6(240 + 60pi) = 40 + 10 pi

hence B
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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02 Dec 2014, 23:48
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Hi,

I am unable to understand the solution of this question. Diameter of the semicircle is not given. However, diameter = 60 is being assumed by all solution providers. Kindly explain it in details. I will be grateful if anyone looks into this.
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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02 Dec 2014, 23:58
deya wrote:
Hi,

I am unable to understand the solution of this question. Diameter of the semicircle is not given. However, diameter = 60 is being assumed by all solution providers. Kindly explain it in details. I will be grateful if anyone looks into this.

Split the figure in 2 semicircles & 1 rectangle.

You get diameter = 60

It has been calculated; not assumed
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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04 Jun 2017, 12:00
Why Distance covered in 42 seconds is 240+60π? I think It should be 1/4 of overall distance (240 + 60п)/4
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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04 Jun 2017, 17:47
4
The answer has to be a factor of the perimeter i.e. 240+60pi.
Now 240+60pi = 6(40+10pi).
Only B satisfies this condition. No other calculation required.
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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04 Jun 2017, 22:30
batyroff wrote:
Why Distance covered in 42 seconds is 240+60π? I think It should be 1/4 of overall distance (240 + 60п)/4

Hi

It is mentioned that its a 4-lap relay race.. which means every team member would run the entire lap (which is calculated already by many as 240+60п).

The table shows lap times for each runner, which means the times depicted are the times taken by each runner to run the complete lap, individually.

hope it helps.
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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25 Jun 2017, 01:43
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Can anyone please explain why the 4th member alone of team B is considered for running in delayed time?

By the question, I assumed/understood that all people of team B are running at the same time in competition with team A people. Then, why only 4th member race time is considered?
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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07 Oct 2018, 20:17
ankitsood5 wrote:
The answer has to be a factor of the perimeter i.e. 240+60pi.
Now 240+60pi = 6(40+10pi).
Only B satisfies this condition. No other calculation required.

Please explain why it has to be a factor.
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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13 Oct 2018, 20:37
1
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Why is the distance to be covered in last 7 seconds found out by using 42 sec (time of team B player) and not by 41sec?
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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13 Oct 2018, 21:06
1
smratikasharma wrote:
Why is the distance to be covered in last 7 seconds found out by using 42 sec (time of team B player) and not by 41sec?

Team A wins the race (That is after 178th second whatever distance is left will be the,distance left by Team B to cover the distance.So,this lag is from Team B which has to make up.

Press Kudos if it helps!!
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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12 Nov 2018, 06:17
I did it by a shortcut. So I know that the total distance for one round is (pi + 4) * 60. I just searched in the answer choices the ratio of the constant of pi and the constant in the parenthesis should be 1:4 respectively. Only B matches the answer.
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Re: The figure below represents a track with identical semi-circular ends  [#permalink]

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14 Nov 2019, 23:25
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Re: The figure below represents a track with identical semi-circular ends   [#permalink] 14 Nov 2019, 23:25