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Bunuel
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Two persons A and B are racing along a circular track. The speed of A 18 Jan 2022, 07:00
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Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.

A. 27 minutes
B. 19 minutes
C. 13.5 minutes
D. 12 minutes
E. 9.5 minutes




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C
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Two persons A and B are racing along a circular track. The speed of A 10 Mar 2022, 19:26
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Bunuel
Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.

A. 27 minutes
B. 19 minutes
C. 13.5 minutes
D. 12 minutes
E. 9.5 minutes




Are You Up For the Challenge: 700 Level Questions
Show more

When two people are running on a circular track in the same direction, when will they meet for the first time after starting? Think about it - the faster one gets ahead the moment they start. He keeps increasing the distance between them with time. If it were a straight line race, he would just keep increasing distance between them. But since its a circular track, when the distance between them becomes equal to the circumference of the circle, they are together at the same point again. So, they meet for the first time when the faster one covers exactly one lap more than the slower one.
So if their speeds are in the ratio 2:1, the number of laps covered by them (effectively the distance covered by them) will also be in the ratio 2:1 in the same time.
This means when the faster one covered 1 lap, the slower one covers half a lap. When the faster one covers 2 laps, the slower one covers 1 lap, when the faster one covers 3 laps, the slower one covers 1.5 laps, when the faster one covers 4 laps, the slower one covers 2 laps and so on...
So the faster one would have covered exactly 1 lap more than the slower one when the faster one would have covered 2 laps and the slower one would have covered 1 lap. This is when they will meet for the first time after starting.
A does this in 3 mins which means that A has covered 2 laps in 3 mins. To cover 7200/800 = 9 laps, A would need 3*9/2 = 13.5 mins

Answer (C)
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Two persons A and B are racing along a circular track. The speed of A 28 Jan 2022, 11:29
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As both A and B start at the same time from the same place, the speed gives the distance travelled in 3 minutes.
That is, in 3 mins, A travelled 2 x Distance travelled by B.
As they meet in 3 mins, it would be at the starting point. Therefore, in 3 mins A travelled = 2x800m = 1600m and B travelled 800m.
Now, speed of A = 1600 metres/3mins.
Therefore time taken for 7200metres = 7200 x 3/1600 = 13.5 minutes. (Answer C)
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Two persons A and B are racing along a circular track. The speed of A 10 Mar 2022, 12:23
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rapidash
As both A and B start at the same time from the same place, the speed gives the distance travelled in 3 minutes.
That is, in 3 mins, A travelled 2 x Distance travelled by B.
As they meet in 3 mins, it would be at the starting point. Therefore, in 3 mins A travelled = 2x800m = 1600m and B travelled 800m.
Now, speed of A = 1600 metres/3mins.
Therefore time taken for 7200metres = 7200 x 3/1600 = 13.5 minutes. (Answer C)
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rapidash Bunuel KarishmaB
Can you help me explain That is, in 3 mins, A travelled 2 x Distance travelled by B. which is correctly said as Speed Relation but this x could be any multiple so why are we considering only one lap i.e. 800, can also be 1600 and 3200?
Also, why do we say when A and B meet for the first time in circular loops, the faster one has covered 1 lap more than the slower.
Thank you for your help
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Two persons A and B are racing along a circular track. The speed of A 11 Mar 2022, 01:12
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Bunuel
Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.

A. 27 minutes
B. 19 minutes
C. 13.5 minutes
D. 12 minutes
E. 9.5 minutes




Are You Up For the Challenge: 700 Level Questions

When two people are running on a circular track in the same direction, when will they meet for the first time after starting? Think about it - the faster one gets ahead the moment they start. He keeps increasing the distance between them with time. If it were a straight line race, he would just keep increasing distance between them. But since its a circular track, when the distance between them becomes equal to the circumference of the circle, they are together at the same point again. So, they meet for the first time when the faster one covers exactly one lap more than the slower one.
So if their speeds are in the ratio 2:1, the number of laps covered by them (effectively the distance covered by them) will also be in the ratio 2:1 in the same time.
This means when the faster one covered 1 lap, the slower one covers half a lap. When the faster one covers 2 laps, the slower one covers 1 lap, when the faster one covers 3 laps, the slower one covers 1.5 laps, when the faster one covers 4 laps, the slower one covers 2 laps and so on...
So the faster one would have covered exactly 1 lap more than the slower one when the faster one would have covered 2 laps and the slower one would have covered 1 lap. This is when they will meet for the first time after starting.
A does this in 3 mins which means that A has covered 2 laps in 3 mins. To cover 7200/800 = 9 laps, A would need 3*9/2 = 13.5 mins

Answer (C)
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KarishmaB
Thank you for the great explanation, as soon as the circumference word was said, I understood the whole concept
Cheers
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Two persons A and B are racing along a circular track. The speed of A 17 Mar 2022, 00:50
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We can look at this problem from another perspective. When A and B start off A immediately forges ahead of B. But but A has to catch up with B for their 1st meeting so B technically has a one-lap lead of 800m. If B's speed is 's' meter/minute, A's will be 2s meter/minute so the difference is their speeds is 's' m/m. So the time taken for A to neutralize this lead and catch up with B is 800/(2s-s) which is equal to 3 minutes. So 800/s=3...> s=800/3. Thus, A's speed is 2s=1600/3 and the time taken by A to cover 7200m is 7200/(1600/2)=13.5

ANS: C
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Two persons A and B are racing along a circular track. The speed of A 08 Apr 2024, 05:26
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rapidash
As both A and B start at the same time from the same place, the speed gives the distance travelled in 3 minutes.
That is, in 3 mins, A travelled 2 x Distance travelled by B.
As they meet in 3 mins, it would be at the starting point. Therefore, in 3 mins A travelled = 2x800m = 1600m and B travelled 800m.
Now, speed of A = 1600 metres/3mins.
Therefore time taken for 7200metres = 7200 x 3/1600 = 13.5 minutes. (Answer C)

rapidash Bunuel KarishmaB
Can you help me explain That is, in 3 mins, A travelled 2 x Distance travelled by B. which is correctly said as Speed Relation but this x could be any multiple so why are we considering only one lap i.e. 800, can also be 1600 and 3200?
Also, why do we say when A and B meet for the first time in circular loops, the faster one has covered 1 lap more than the slower.
Thank you for your help
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I agree with you. The above reasoning doesnt work on all cases.

Its much easier to use plane logic when numbers are so friendly.

I assumed, since Speed of A is double of B, distance covered by A would also be double of B in a given time.

So if A coveres 800m, B would cover 400m.

When A covers 1600m, B would have covered 800m, which is coincidently the start of the lap.

If you want a formula for it, know that A will only meet B after completing initial 800m.

The distance covered by A after completing a lap should match distance covered by B.
So you could also write,
(800+x) = 2x where x is the diance covered by B in 3mins.
That lands you the value of x veing 800m.

The above formula holds true for all relation of A&B, you will only replace (2) with the appropriate factor.
So for speed of A being 3 times of B, the equation would be
(800+x) = 3x

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Two persons A and B are racing along a circular track. The speed of A 30 Dec 2024, 01:18
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hi KarishmaB i dont think your answer is right. You are assuming that they meet at the start of track again. But this question does not imply that.
KarishmaB
Bunuel
Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.

A. 27 minutes
B. 19 minutes
C. 13.5 minutes
D. 12 minutes
E. 9.5 minutes




Are You Up For the Challenge: 700 Level Questions

When two people are running on a circular track in the same direction, when will they meet for the first time after starting? Think about it - the faster one gets ahead the moment they start. He keeps increasing the distance between them with time. If it were a straight line race, he would just keep increasing distance between them. But since its a circular track, when the distance between them becomes equal to the circumference of the circle, they are together at the same point again. So, they meet for the first time when the faster one covers exactly one lap more than the slower one.
So if their speeds are in the ratio 2:1, the number of laps covered by them (effectively the distance covered by them) will also be in the ratio 2:1 in the same time.
This means when the faster one covered 1 lap, the slower one covers half a lap. When the faster one covers 2 laps, the slower one covers 1 lap, when the faster one covers 3 laps, the slower one covers 1.5 laps, when the faster one covers 4 laps, the slower one covers 2 laps and so on...
So the faster one would have covered exactly 1 lap more than the slower one when the faster one would have covered 2 laps and the slower one would have covered 1 lap. This is when they will meet for the first time after starting.
A does this in 3 mins which means that A has covered 2 laps in 3 mins. To cover 7200/800 = 9 laps, A would need 3*9/2 = 13.5 mins

Answer (C)
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Two persons A and B are racing along a circular track. The speed of A 30 Dec 2024, 02:09
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hi MartyMurray Bunuel - what is the justification/understanding that where they meet = start point? I would think that they could meet at different points given different speeds.
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hi KarishmaB i dont think your answer is right. You are assuming that they meet at the start of track again. But this question does not imply that.
KarishmaB
Bunuel
Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.

A. 27 minutes
B. 19 minutes
C. 13.5 minutes
D. 12 minutes
E. 9.5 minutes




Are You Up For the Challenge: 700 Level Questions

When two people are running on a circular track in the same direction, when will they meet for the first time after starting? Think about it - the faster one gets ahead the moment they start. He keeps increasing the distance between them with time. If it were a straight line race, he would just keep increasing distance between them. But since its a circular track, when the distance between them becomes equal to the circumference of the circle, they are together at the same point again. So, they meet for the first time when the faster one covers exactly one lap more than the slower one.
So if their speeds are in the ratio 2:1, the number of laps covered by them (effectively the distance covered by them) will also be in the ratio 2:1 in the same time.
This means when the faster one covered 1 lap, the slower one covers half a lap. When the faster one covers 2 laps, the slower one covers 1 lap, when the faster one covers 3 laps, the slower one covers 1.5 laps, when the faster one covers 4 laps, the slower one covers 2 laps and so on...
So the faster one would have covered exactly 1 lap more than the slower one when the faster one would have covered 2 laps and the slower one would have covered 1 lap. This is when they will meet for the first time after starting.
A does this in 3 mins which means that A has covered 2 laps in 3 mins. To cover 7200/800 = 9 laps, A would need 3*9/2 = 13.5 mins

Answer (C)
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You can infer from the given data that they meet at the starting point. I have explained why in my solution above.
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Two persons A and B are racing along a circular track. The speed of A 05 Oct 2025, 07:15
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I got confused with:
"After the start of the race, A meets B for the first time at the end of the third minute."

From that I understand that the distance travelled by A at t=3min59sec is equal to the distance travelled by B plus 800m.

But everyone did the same math with t=3min.

Can someome explain why the bold part is equal 3min. :)
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Two persons A and B are racing along a circular track. The speed of A 05 Oct 2025, 07:45
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Diegomorande
I got confused with:
"After the start of the race, A meets B for the first time at the end of the third minute."

From that I understand that the distance travelled by A at t=3min59sec is equal to the distance travelled by B plus 800m.

But everyone did the same math with t=3min.

Can someome explain why the bold part is equal 3min. :)
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“End of the third minute” means exactly 3 minutes have passed. It refers to the completion of the third minute, not the 3:59 mark. So t = 3 minutes, not 3 minutes and 59 seconds.
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Two persons A and B are racing along a circular track. The speed of A 05 Oct 2025, 08:03
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thanks for the quick reply! it makes sense now
Bunuel

“End of the third minute” means exactly 3 minutes have passed. It refers to the completion of the third minute, not the 3:59 mark. So t = 3 minutes, not 3 minutes and 59 seconds.
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