n a 3600 m race around a circular track of length 400m, the faster run

Question

n a 3600 m race around a circular track of length 400m, the faster runner and the slowest runner meet at the end of the fourth minute, for the first time after the start of the race. All the runners maintain uniform speed throughout the race. If the faster runner runs at thrice the speed of the slowest runner. Find the time taken by the faster runner to finish the race.

A. 36 minute
B. 24 minute
C. 16 minute
D. 12 minute
E. 10 minute

A. 36 minute
B. 24 minute
C. 16 minute
D. 12 minute
E. 10 minute

nick1816 · Answer

Speed of the fastest runner=3v
speed of the slowest runner= v

Relative distance covered by fastest runner to cross the slowest runner for the first time = 400m
relative speed= 3v-v=2v

400/2v=4
v= 50m/min

speed of fastest runner= 3*50=150m/mim

Time taken by the fastest runner to complete the race= 3600/150=24min

vs224 · Answer

How do you know that racers are running in opposite direction?
What if they are running in same direction.

nick1816 · Answer

1. In a race, you don't suppose to run in an opposite direction. 
2. Because they are running in the same direction, you have to subtract the speed of the runners to find the relative speed.

Archit3110 · Answer

distance = 3600 m
lap distance = 400 m
relative speed ; 3s-s; 2s
time they meet first ; 4 min
so ; 4 = 400/2s ; s = 50 mtr/min
so speed of fast runner per min ; 50*3 ; 150 mtr /min
time fast runner shall take to complete race ; 3600/150 = 24 min
IMO B

ankitprad · Answer

Hi Archit ,

Could you explain how you arrived at this " 4 = 400/2s" ? 
I understand that the total distance covered relatively by the fastest runner in 4 minutes will be 2s * 4 mins, how how is this equal to 400. Wouldn't this imply that the extra distance covered by the fastest runner compared to the the slowest is is one whole lap. I don't think we know this as a fact from the question stem, do we?

Thanks so much

Archit3110 · Answer

ankitprad 
Wouldn't this imply that the extra distance covered by the fastest runner compared to the the slowest is is one whole lap
. we are measuring time in terms of relative speed for every 400 mtrs..

for time 4
distance 400 
and relative speed 2s
we have 4=400/2s ; s =50
hope this helps

Kinshook · Answer

Given:
1. In a 3600 m race around a circular track of length 400m, the faster runner and the slowest runner meet at the end of the fourth minute, for the first time after the start of the race.
2. All the runners maintain uniform speed throughout the race.

Asked: If the faster runner runs at thrice the speed of the slowest runner. Find the time taken by the faster runner to finish the race.

Let the speed of the slowest and the fastest runner be x and 3x m/s respectively

In the race there are 9 laps of 400 m each totalling 3600m .

Relative speed = 3x - x = 2x m/s
Distance = time * speed
400 = 4*60 2x
x = 10/12= 5/6 m/s

Speed of the slowest runner = x = = 5/6 m/s
Speed of the fastest runner = 3x = 5/2 = 2.5 m/s

Time taken by the fastest runner to finish the race = 3600/2.5 = 1440 seconds = 24 mins

IMO B

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n a 3600 m race around a circular track of length 400m, the faster run

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