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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 run

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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 run

by Vincen » Fri Jun 19, 2020 2:30 am

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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

[spoiler]OA=B[/spoiler]

Source: Veritas Prep
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Re: Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael

by Brent@GMATPrepNow » Fri Jun 19, 2020 5:30 am
Vincen wrote: ↑
Fri Jun 19, 2020 2:30 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

[spoiler]OA=B[/spoiler]

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

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Brent
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Re: Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael

by swerve » Fri Jun 19, 2020 10:01 am
Vincen wrote: ↑
Fri Jun 19, 2020 2:30 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

[spoiler]OA=B[/spoiler]

Source: Veritas Prep
Michael makes a lap in 40 seconds. He makes \(x\) laps. Time spent on road \(= 40x\)
When Michael reaches Donovan, Donovan has made exactly 1 lap less. It takes him \(45\) seconds to make a lap. Total time spent on road \(= 45(x-1)\)
\(40x=45(x-1)\)
\(5x=45\)
\(x=9\) laps

Therefore, B
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