circular meter track

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nidhis.1408: Master | Next Rank: 500 Posts; Posts: 135; Joined: Mon Oct 03, 2011 6:54 amFollowed by: 4 members

by nidhis.1408 » Wed Oct 17, 2012 7:03 am

Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

a. 8
b. 9
c. 10
d.11
e. 12

Can anyone please explain this problem with explanation.

A similar problem-
Florence and Jackie are running laps on a circular quarter-mile track. If Florence completes each lap in 75 seconds and Jackie completes each lap in 90 seconds, how many laps will Jackie have run before she's passed by Florence, assuming they start at the same time.

a. 5
b. 6
c. 7
d. 8
e. 9

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Source: Beat The GMAT — Problem Solving | Wed Oct 17, 2012 7:03 am

gmat6087: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Sat Oct 29, 2011 3:49 amFollowed by: 1 member; Thanked: 2 times

by gmat6087 » Wed Oct 17, 2012 7:36 am

nidhis.1408 wrote:Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

a. 8
b. 9
c. 10
d.11
e. 12

Can anyone please explain this problem with explanation.

A similar problem-
Florence and Jackie are running laps on a circular quarter-mile track. If Florence completes each lap in 75 seconds and Jackie completes each lap in 90 seconds, how many laps will Jackie have run before she's passed by Florence, assuming they start at the same time.

a. 5
b. 6
c. 7
d. 8
e. 9

LCM of 40,45=360
SO they will meet in 360th second after they start to run.
360/40=9 sec
40 secs taken to complete one round to how many rounds total taken in 360 secs is 360/40=9 secs.

Whats the OA.

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nidhis.1408: Master | Next Rank: 500 Posts; Posts: 135; Joined: Mon Oct 03, 2011 6:54 amFollowed by: 4 members

by nidhis.1408 » Wed Oct 17, 2012 7:39 am

9 is the answer and answer for second problem is 5

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 17, 2012 7:41 am

nidhis.1408 wrote:Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

a. 8
b. 9
c. 10
d.11
e. 12

To catch up to Donovan, Michael must complete 1 more lap than Donovan in the same amount of time.
We can plug in the answers, which represent the number of laps that must be completed by Michael.

Answer choice C: 10 laps
Time for Michael to complete 10 laps = 10*40 = 400 seconds.
Number of laps completed by Donovan in 400 seconds = 400/45 = 80/9 = 8.8.
Michael's laps - Donovan's laps = 10 - 8.8 = 1.2.
No good.
Since Michael has completed 1.2 more laps than Donovan, he is now .2 laps AHEAD of Donovan.
To catch up to Donovan without pulling ahead, Michael must complete FEWER laps.
Eliminate C, D, and E.

Answer choice B: 9 laps
Time for Michael to complete 9 laps = 9*40 = 360 seconds.
Number of laps completed by Donovan in 360 seconds = 360/45 = 8.
Michael's laps - Donovan's laps = 9-8 = 1.
Success!

The correct answer is B.

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anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Wed Oct 17, 2012 7:44 am

gmat6087 wrote:
nidhis.1408 wrote:Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

a. 8
b. 9
c. 10
d.11
e. 12

Can anyone please explain this problem with explanation.

A similar problem-
Florence and Jackie are running laps on a circular quarter-mile track. If Florence completes each lap in 75 seconds and Jackie completes each lap in 90 seconds, how many laps will Jackie have run before she's passed by Florence, assuming they start at the same time.

a. 5
b. 6
c. 7
d. 8
e. 9

LCM of 40,45=360
SO they will meet in 360th second after they start to run.
360/40=9 sec
40 secs taken to complete one round to how many rounds total taken in 360 secs is 360/40=9 secs.

Whats the OA.

I am not nit picking, but you mean 9 laps - Michael has to run.

Regards
Anup

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