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Bunuel
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A and B stand at distinct points of a circular race track of length 12 09 Dec 2021, 09:15
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A and B stand at distinct points of a circular race track of length 120 meters. They run at speeds of 'a' meter per second and 'b' meter per second respectively. They meet for the first time 16 seconds after they started the race and for the second time 40 seconds from the time they started the race. If B had started in the opposite direction to the one he originally started, they would have met for the first time after 40 seconds. If B is quicker than A, find B’s speed (in meter per second).

A. 3
B. 4
C. 5
D. 8
E. 10


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chetan2u
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A and B stand at distinct points of a circular race track of length 12 04 Feb 2022, 19:42
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Bunuel
A and B stand at distinct points of a circular race track of length 120 meters. They run at speeds of 'a' meter per second and 'b' meter per second respectively. They meet for the first time 16 seconds after they started the race and for the second time 40 seconds from the time they started the race. If B had started in the opposite direction to the one he originally started, they would have met for the first time after 40 seconds. If B is quicker than A, find B’s speed (in meter per second).

A. 3
B. 4
C. 5
D. 8
E. 10


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When both are moving towards each other
They meet for the first time in 16 seconds and second time in 40 seconds.
Thus, they cover entire lap in 40-16 or 24 seconds within themselves. =>
Combined speed = 120/24 = 5m/s => a+b = 5

Since they meet after 16 seconds, they are 16*5 or 80 m away from each other when they run towards each other.
This means that the distance between then when they are running in same direction is 120-80 or 40m.

When both are moving in same direction
b covers 40m extra in 40 seconds, that is b’s speed is 40/40 or 1m/s more than that of a. => b=a+1

a+b=5 and b=a+1
Thus, a=2 and b=3.


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Anurocks1233
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A and B stand at distinct points of a circular race track of length 12 10 Dec 2021, 06:42
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Posting the solution from one note

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FE8AF533-227B-4CC0-8B60-71E0E6C916D3.jpeg
FE8AF533-227B-4CC0-8B60-71E0E6C916D3.jpeg [ 733.96 KiB | Viewed 8200 times ]

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A and B stand at distinct points of a circular race track of length 12 10 Dec 2021, 09:59
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Anurocks1233

Can you please elaborate few more on the steps you did:-

\(\frac{x}{(a+b)}\) = \(16\) --> How did you reach this expression.. what is x here (I am assuming this is the first time they meet -- x distance in 16 seconds.. but why it's a+b, shouldnt it be a-b as track is circular?)

\(x=20\) --> How did you get this value. --> (If you considered (a+b) = 5 m/s ; then x should have been 80)

\(\frac{120-x}{b-a }= 40\) [Reverse] --> what do u mean by reverse

where did you use the relative speed 5m/s
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A and B stand at distinct points of a circular race track of length 12 10 Dec 2021, 11:40
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rsrighosh
Anurocks1233

Can you please elaborate few more on the steps you did:-

\(\frac{x}{(a+b)}\) = \(16\) --> How did you reach this expression.. what is x here (I am assuming this is the first time they meet -- x distance in 16 seconds.. but why it's a+b, shouldnt it be a-b as track is circular?)
a+b because we know that this time is quicker vs the time it took to meet them first time when B ran in the reverse direction.

\(x=20\) --> How did you get this value. --> (If you considered (a+b) = 5 m/s ; then x should have been 80)
I see X=80 in my solution. there is no x=20.

\(\frac{120-x}{b-a }= 40\) [Reverse] --> what do u mean by reverse
Reverse when B reverse the direction.

where did you use the relative speed 5m/s
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The first x=80 we got is from the relative speed. I used that term because I did not deduce at that point which direction A and B running as there are two possibilities: running toward each other and running away from each other.

I hope this make sense and let me know if you have any other follow up on this!
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A and B stand at distinct points of a circular race track of length 12 30 Dec 2024, 01:55
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Not really following your answer. What is the maths behind them covering a whole lap in 24s? Why is combined speed 120/24=5? A lot of unsaid assumptions/gaps unfortunately...
chetan2u
Bunuel
A and B stand at distinct points of a circular race track of length 120 meters. They run at speeds of 'a' meter per second and 'b' meter per second respectively. They meet for the first time 16 seconds after they started the race and for the second time 40 seconds from the time they started the race. If B had started in the opposite direction to the one he originally started, they would have met for the first time after 40 seconds. If B is quicker than A, find B’s speed (in meter per second).

A. 3
B. 4
C. 5
D. 8
E. 10


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When both are moving towards each other
They meet for the first time in 16 seconds and second time in 40 seconds.
Thus, they cover entire lap in 40-16 or 24 seconds within themselves. =>
Combined speed = 120/24 = 5m/s => a+b = 5

Since they meet after 16 seconds, they are 16*5 or 80 m away from each other when they run towards each other.
This means that the distance between then when they are running in same direction is 120-80 or 40m.

When both are moving in same direction
b covers 40m extra in 40 seconds, that is b’s speed is 40/40 or 1m/s more than that of a. => b=a+1

a+b=5 and b=a+1
Thus, a=2 and b=3.


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A and B stand at distinct points of a circular race track of length 12 03 Jan 2025, 09:50
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Bunuel it is not clear "If B had started in the opposite direction to the one he originally started,", when first time they started they started in same direction or opposite direction?
If someone take first meet and second meet as same direction move and last one take different direction move, question is different.
I think it is really needed to change the words properly. Otherwise it is very confusing.
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