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Donovan and Michael are racing around a circular 400-meter

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Donovan and Michael are racing around a circular 400-meter

by BTGmoderatorDC » Wed Jul 31, 2019 5:29 pm

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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

OA B

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by Jay@ManhattanReview » Wed Jul 31, 2019 11:39 pm
BTGmoderatorDC 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

OA B

Source: Veritas Prep
We know that Donovan runs faster than Michael, so Donovan will always be ahead of Michael. We have to find out the number of laps Donovan would complete when they both are together at the same point again. It is obvious that the number of laps Donovan completes is greater than what Michael does.

Since Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, they would be together for the first time = LCM of 40 and 45 seconds = 360 seconds.

Thus, the number of laps Michael completes in 360 seconds = 360/40 = 9 laps.

The correct answer: B

Hope this helps!

-Jay
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by GMATGuruNY » Thu Aug 01, 2019 2:01 am
BTGmoderatorDC 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.
When the correct answer is plugged in, Michael will complete 1 more lap than Donovan.

Answer choice D: 11 laps
Since Michael completes 1 lap every 40 seconds, the time for Michael to complete 11 laps = 11*40 = 440 seconds.
Since Donovan completes 1 lap every 45 seconds, the number of laps completed by Donovan in 440 seconds = 440/45 = 85/9 ≈ 9.7
Michael's laps - Donovan's laps ≈ 11 - 9.7 = 1.3
No good.
Since Michael has completed about 1.3 more laps than Donovan, he is now about 0.3 laps AHEAD of Donovan.
To catch up to Donovan without pulling ahead, Michael must complete FEWER laps.
Eliminate D and E.

Answer choice B: 9 laps
Since Michael completes 1 lap every 40 seconds, the time for Michael to complete = 9 laps = 9*40 = 360 seconds.
Since Donovan completes 1 lap every 45 seconds, the 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 Scott@TargetTestPrep » Sun Aug 04, 2019 10:28 am
BTGmoderatorDC 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

OA B

Source: Veritas Prep
We are given that Donovan runs each lap in 45 seconds, and Michael runs each lap in 40 seconds. Thus, their respective speeds are 400/45 = 80/9 meters per second and 400/40 = 10 meters per second.

If Michael passes Donovan t seconds after they start running, he will have traveled exactly 400 meters more than Donovan (because 400 meters is equal to one lap). Since distance = rate x time, we can say that in t seconds, Donovan covers a distance of 80t/9 meters, and Michael covers a distance of 10t meters. Since the difference between these distances has to equal 400, we have the following:

10t - 80t/9 = 400

90t/9 - 80t/9 = 400

10t/9 = 400

10t = 3600

t = 360 seconds

In 360 seconds, Michael completes 360/40 = 9 laps.

Answer: B

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Re: Donovan and Michael are racing around a circular 400-meter

by Brent@GMATPrepNow » Sun Jan 19, 2020 12:25 pm
BTGmoderatorDC wrote: ↑
Wed Jul 31, 2019 5:29 pm
 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

OA B

Source: Veritas Prep
If Michael passes Donovan, then Donovan completes ONE LAP LESS than Michael completes IN THE SAME AMOUNT OF TIME.
So, if x = # of laps Michael completes, then....
x - 1 = # of laps Donovan completes.

So, we can write the following WORD EQUATION:
(time for Michael to complete x laps) = (time for Donovan to complete x - 1 laps)
It takes 40 seconds for Michael to complete EACH lap, and it takes 45 seconds for Donovan to complete EACH lap.
So, we get: (40)(x) = (45)(x - 1)
Expand: 40x = 45x - 45
Solve to get x = 9

So, Michael must complete 9 laps

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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