Tim and Glenn are running laps around a circular track. If they start

Question

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.

Mo2men · Accepted Answer

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.

Answer: A

KarishmaParmar · Answer

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.

MartyTargetTestPrep · Answer

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.

The correct answer is A.

PrakharGMAT · Answer

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

/ 48 = (N*X) / 60

But not able to solve further.
Can you please help..?

chetan2u · Answer

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

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

PrakharGMAT · Answer

Thank you so much  chetan2u .

I made it too complicated..

nikhiljd · Answer

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 ...

if nothing else pops in the head ...

ishan92 · Answer

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

EMPOWERgmatRichC · Answer

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

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

kajaldaryani46 · Answer

——-
Hi  Bunuel ,

Could u pls link similar Qs related to circular track Qs below

Posted from my mobile device

Bunuel · Answer

Basshead · Answer

(1) Tim completes a lap in 4/5th of a minute. In one minute, Tim completes 5/4 of a lap.

In one minute, Glenn completes 1 lap.

For every minute, Tim gets closer to Glenn by 1/4th of a lap. Therefore, after 4 minutes Tim is exactly one lap ahead of Glen.

(2) Insufficient.

ConquerGMAT007 · Answer

Q. 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.

Ans.
 Given 
Tim Speed> Glenn Speed

Req.: Time taken by Tim to catch Glenn while the distance is 1 full lap -->d (let's say)

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

Let lap be = d
Tim Speed = d/48
Glenn Speed = d/60

Relative speed = Tim Seed - Glenn Speed 
= d/48 - d/60

Time = Distance / Relative speed = d/ (d/48 - d/60) ----  Sufficient

(2) The track is 400 meters in circumference.  -- No individual time given hence  insufficient

pierjoejoe · Answer

i have a BIG doubt. the question is

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.

THE question  does not tell us if they start at the same point of the track , just that they start simulteneusly. HOW can we answer this question. the info should not be sufficient to answer.  Bunuel  please help me here.

Bunuel · Answer

The wording could have been better. However, if we interpret "further" to mean more, so in how many seconds will Tim have run exactly one lap more than Glenn, the answer would still be A. In 240 seconds, Tim runs 5 laps, and Glenn runs 4 laps, irrespective of where they start or the direction of running.

pierjoejoe · Answer

that's true. so in the case where the problem asks 1 lap further, we have to consider the GAP that needs to be "shrinked" is still 1 lenght of the circular track, even if the 2 start from different positions..

while in the case where the problem asks for example the time it takes to overtake one another, in that case we need to know the initial position. is it right?

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Tim and Glenn are running laps around a circular track. If they start

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Tim and Glenn are running laps around a circular track. If they start

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards