Race

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 7:20 am

In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

a) 20 min
b) 15 min
c) 10 min
d) 5 min
e) 4 min

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 7:20 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 7:29 am

shashank.ism wrote:In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

a) 20 min
b) 15 min
c) 10 min
d) 5 min
e) 4 min

Imp. pt. to be kept in the mind:-The fastest runner is leading by a whole circumference at the 5th minute.
So,relative speed = F(fastest)-S(slowest)
relative time = 5min. = 300 seconds
relative distance = 1000
also,F=2S
Hence,by solving 2S - S = 1000/5 = 200 (metres/min.)

TIME TAKEN TO FINISH THE RACE =[spoiler] 4000 / 400 = 10 min. C[/spoiler]

Last edited by harsh.champ on Mon Feb 08, 2010 11:06 am, edited 2 times in total.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 10:49 am

shashank.ism wrote:In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

a) 20 min
b) 15 min
c) 10 min
d) 5 min
e) 4 min

Fastest runner has double the speed of slowest and they meet at the end of 5 mins

The difference in distance covered btw fastest and slowest = 1 lap when they meet
Since the speed of fastest is double of slowest he must have run two laps by that time

Time required for him to finish the race = 5+5 = 10 minutes

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