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16 Feb 2015, 06:59
Kudos
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B
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Difficulty:
55%
(hard)
Question Stats:
65% (02:12) correct
35%
(02:27)
wrong
based on 987
sessions
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Not Attempted Yet
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
A. 8
B. 9
C. 10
D. 11
E. 12
16 Feb 2015, 21:08
Kudos
Bookmarks
@
Simply take the LCM of 40 and 45 - you get 360. This is the time they will take to meet for the first time. In this time, Michael would have covered 360/40 = 9 laps.
Answer (B)
The reason for this:
Judging from the question, we know that Michael and Donovan are running in the same direction. When will Michael overtake Donovan? Michael will always be a bit ahead of Donovan and will keep increasing this distance between them till the time he completes one full lap more than Donovan. That is when they will both again be at the starting point together. The time that should have passed at this point should be a multiple of both 40 and 45 so that they are at the starting point. So we find the LCM of 40 and 45 which is 360. In this time, Donovan completes 360/45 = 8 laps and Michael completes 360/40 = 9 laps.
Bunuel
Simply take the LCM of 40 and 45 - you get 360. This is the time they will take to meet for the first time. In this time, Michael would have covered 360/40 = 9 laps.
Answer (B)
The reason for this:
Judging from the question, we know that Michael and Donovan are running in the same direction. When will Michael overtake Donovan? Michael will always be a bit ahead of Donovan and will keep increasing this distance between them till the time he completes one full lap more than Donovan. That is when they will both again be at the starting point together. The time that should have passed at this point should be a multiple of both 40 and 45 so that they are at the starting point. So we find the LCM of 40 and 45 which is 360. In this time, Donovan completes 360/45 = 8 laps and Michael completes 360/40 = 9 laps.
16 Feb 2015, 07:36
Kudos
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Bunuel
As per options given, Assuming that the two runners are running along the track in the SAME DIRECTION
Speed of Michael = Distance/Time = 400/40 = 10 m/Sec
Speed of Donovan = Distance/Time = 400/45 = 80/9 m/Sec
Relative Speed for the two objects moving in the same direction = Difference between their speed
Note: Relative Speed = The rate at which the distance between the two moving objects increases or decreases
In same Direction, The Distance Increases at lower rate, and the Rate = S1 - S2
In Opposite Direction, The Distance Increases at Higher rate, and the Rate = S1 + S2
Hence Relative Speed of Michael and Donovan = 10 - (80/9) = 10/9 m/sec
Relative Distance to be covered by Michael to pass Donovan = Length of complete Track = 400 mt
Time Taken by Michael to pass Donovan = Relative Distance / Relative Speed = 400 / (10/9) = 360 Secs
No. of Laps completed by Michael in 360 Secs = Total Time to pass Donovan / Time of Michael per Lap = 360/40 = 9
Answer: Option
