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Math Expert V
Joined: 02 Sep 2009
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Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Difficulty:   15% (low)

Question Stats: 76% (01:12) correct 24% (01:22) wrong based on 247 sessions

### HideShow timer Statistics Tim and Glenn are running laps around a circular track. If they start at exactly the same time, in how many seconds will Tim have run exactly one lap further than Glenn?

(1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

(2) The track is 400 meters in circumference.

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GMAT 1: 710 Q48 V40 Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Bunuel wrote:
Tim and Glenn are running laps around a circular track. If they start at exactly the same time, in how many seconds will Tim have run exactly one lap further than Glenn?

(1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

(2) The track is 400 meters in circumference.

I will really answer this question intuitively.If it were tim runs one lap in one minute and glen one lap in two minutes, i would know the answer of the question asked by only this much information.

So I think A is sufficient.
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Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Bunuel wrote:
Tim and Glenn are running laps around a circular track. If they start at exactly the same time, in how many seconds will Tim have run exactly one lap further than Glenn?

(1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

(2) The track is 400 meters in circumference.

Fact 2: Just circumference. Neither time nor speeds............Insuff

Fact 1: As we have rate of everyone, we can reach the time required. I will construct a table for every time interval (60 sec) to calculate the laps run by Tim and Glenn

Glenn will run 1 lap after 60 sec, 2 laps after 120 sec.............4 laps after 240 sec.

Time will run 1.25 lap after 60 sec, 2.5 lap after 120 sec ........5 laps after 240 sec.

Tim will take 240 second to run exactly one lap further than Glenn.

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GMAT 1: 800 Q51 V51 Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Statement 1 tells us that every 60 seconds Tim runs 1 1/4 lap while Glen runs 1 lap. So after 4 x 60 = 240 seconds, Tim will have run a full lap more than Glen has.

Sufficient.

Statement 2 gives no information regarding their relative rates.

Insufficient.

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Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Mo2men wrote:
Bunuel wrote:
Tim and Glenn are running laps around a circular track. If they start at exactly the same time, in how many seconds will Tim have run exactly one lap further than Glenn?

(1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

(2) The track is 400 meters in circumference.

Fact 2: Just circumference. Neither time nor speeds............Insuff

Fact 1: As we have rate of everyone, we can reach the time required. I will construct a table for every time interval (60 sec) to calculate the laps run by Tim and Glenn

Glenn will run 1 lap after 60 sec, 2 laps after 120 sec.............4 laps after 240 sec.

Time will run 1.25 lap after 60 sec, 2.5 lap after 120 sec ........5 laps after 240 sec.

Tim will take 240 second to run exactly one lap further than Glenn.

Can we consider lap length of both people equal.
Manager  Joined: 12 Jan 2015
Posts: 196
Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Hi Experts / Bunuel / chetan2u,

Statment 1

I tried to make an equation by which we can straightaway get the answer as 240 sec, but couldn't.
In this case both the candidates Tim and Glen will take the same no of seconds so I equate them.

Let
N= No of rounds
X= Distance of 1 round

No of rounds taken by Tim= (N*X) + 1
Speed of Tim = 48 sec.
No of rounds taken by Glen = N*X
Speed of Tim = 60 sec.

I equate them because both will run same no of seconds.
Time taken by Tim = Time taken by Glen

Distance covered by Tim / Speed of Tim = Distance covered by Glen/ Speed of Glen

[(N*X) + 1 ] / 48 = (N*X) / 60

But not able to solve further.
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Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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PrakharGMAT wrote:
Hi Experts / Bunuel / chetan2u,

Statment 1

I tried to make an equation by which we can straightaway get the answer as 240 sec, but couldn't.
In this case both the candidates Tim and Glen will take the same no of seconds so I equate them.

Let
N= No of rounds
X= Distance of 1 round

No of rounds taken by Tim= (N*X) + 1
Speed of Tim = 48 sec.
No of rounds taken by Glen = N*X
Speed of Tim = 60 sec.

I equate them because both will run same no of seconds.
Time taken by Tim = Time taken by Glen

Distance covered by Tim / Speed of Tim = Distance covered by Glen/ Speed of Glen

[(N*X) + 1 ] / 48 = (N*X) / 60

But not able to solve further.

Hi,
you are doing two wrong things here..
1) firstly 48 sec and 60 sec is TIME and not SPEED..
2) secondly if I take what you have written

Quote:
Let
N= No of rounds
X= Distance of 1 round

No of rounds taken by Tim= (N*X) + 1 (N+1)... you have to increase the round N by 1 and not the entire distance NX
Speed Time of Tim to complete one lap = 48 sec.
so total time taken = (N+1)*48
No of rounds taken by Glen =N*X N
Speedof Tim = 60 sec.
so total time taken = N*60

So the solution will be--
time taken to complete the rounds will be the same..
(N+1)*48=N*60..
48N+48=60N..
12N=48, so N= 4..

so time taken = 60N=60*4=240, OR
(N+1)*48=5*48=240 seconds

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Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Thank you so much chetan2u.

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Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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robu wrote:
Mo2men wrote:
Bunuel wrote:
Tim and Glenn are running laps around a circular track. If they start at exactly the same time, in how many seconds will Tim have run exactly one lap further than Glenn?

(1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

(2) The track is 400 meters in circumference.

Fact 2: Just circumference. Neither time nor speeds............Insuff

Fact 1: As we have rate of everyone, we can reach the time required. I will construct a table for every time interval (60 sec) to calculate the laps run by Tim and Glenn

Glenn will run 1 lap after 60 sec, 2 laps after 120 sec.............4 laps after 240 sec.

Time will run 1.25 lap after 60 sec, 2.5 lap after 120 sec ........5 laps after 240 sec.

Tim will take 240 second to run exactly one lap further than Glenn.

Can we consider lap length of both people equal.

Running laps around a circular track means complete track length. Each lap includes complete track length. So, the lap length (one lap = one complete circular track) is considered equal.
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Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Can we use this ..
In a race if we need to find the time taken by the fastest person to lap the other people we can find that using the LCM of all the individual times?
for this qxn P1 =48sec and P2 = 60sec
LCM = 240
so P1 takes 240seconds to overlap P2

Statement 2 obviously gives no info on the rates times etc..
Is this method fine???    if nothing else pops in the head ...
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Joined: 22 Jan 2015
Posts: 22
Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Bunuel wrote:
Tim and Glenn are running laps around a circular track. If they start at exactly the same time, in how many seconds will Tim have run exactly one lap further than Glenn?

(1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

(2) The track is 400 meters in circumference.

We want to know when will Dt-Dg = 2*pi*r

Consider statement (A)
Let the time when it happens be 't'.
Dt-Dg = 2*pi*r
(sT-sG)t = 2*pi*r
2*pi*r/48 - 2*pi*r/60 =2*pi*r
(1/48 - 1/60 ) t =1
t=240 secs
(A) is sufficient
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Tim and Glenn are running laps around a circular track. If they start  [#permalink]

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Hi All,

We're told that Tim and Glenn are running laps around a circular track and that they start at exactly the same time. We're asked in how many seconds will have passed when Tim has run exactly one lap further than Glenn.

This is an example of a rare 'combined rate' question (sometimes called a "chase down" question). The key to these types of questions is to figure out the DIFFERENCE in speeds of the two entities (when they're moving at the same time) and use that number as a basis for comparison.

1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

Here, we know that Tim runs a lap in 48 seconds and Glenn runs a lap in 60 seconds. The difference in their rates is 12 seconds/lap.

Tim will "catch up" 12 seconds on Glenn every lap. Since Glenn needs 60 seconds to finish a lap, Tim needs 60/12 = 5 laps to catch Glenn.

You can see that the results are correct by doing the following math:

Tim: (5 laps)(48 seconds per lap) = 240 seconds

Glenn: (X laps)(60 seconds per lap) = 240 seconds
X = 240/60 = 4 laps

In 240 seconds, Tim runs 5 laps and Glenn runs 4 laps. At this point, Time has "lapped" Glenn.
Fact 1 is SUFFICIENT

2) The track is 400 meters in circumference.

The information in Fact 2 tells us nothing about the two rates, so there's no way to answer the question.
Fact 2 is INSUFFICIENT

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www.empowergmat.com/ Re: Tim and Glenn are running laps around a circular track. If they start   [#permalink] 25 Feb 2018, 15:57
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