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circular meter track

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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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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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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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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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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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