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Two bicycle wheels, A and B, start rotating at constant speeds at the

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Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
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I think the answer should be C.

Statement 1: NOT SUFFICIENT. Assuming the speed of the wheel A= x and B=3x, we cannot determine the individual actual speeds (which are required to answer this question).

Statement 2: NOT SUFFICIENT. The average speed also doesn't help to determine the individual actual speeds (which are required to answer this question).

Putting Statement 1 and Statement 2 together
The individual speeds can be determined by the formula: Average Speed= (S1+S2)/2
40= x+3x/2
x= 20 revolutions per min (Speed of A)
3x= 60 revolutions per min(Speed of B)

Relative Distance= 6 rotations (given in the question stem)
Relative Speed= 60-20 revolutions per min (calculated above)

Time= Relative Distance/Relative Speed
= 6*60/40
= 9 secs

Originally posted by PRAGATIOSTWAL on 23 Apr 2024, 01:55.
Last edited by PRAGATIOSTWAL on 23 Apr 2024, 10:21, edited 2 times in total.
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Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
PRAGATIOSTWAL wrote:
I think the answer should be C.

Statement 1: NOT SUFFICIENT. Assuming the speed of the wheel A= x and B=3x, we cannot determine the individual actual speeds (which are required to answer this question).

Statement 2: NOT SUFFICIENT. The average speed also doesn't help to determine the individual actual speeds (which are required to answer this question).

Putting Statement 1 and Statement 2 together
The individual speeds can be determined by the formula: Average Speed= 2*S1*S2/(S1+S2)
40= 2*x*3x/(x+3x)
x= 80/3 revolutions per min (Speed of A)
3x= 80 revolutions per min(Speed of B)

Relative Distance= 6 rotations (given in the question stem)
Relative Speed= 80-80/3 revolutions per min (calculated above)

Time= Relative Distance/Relative Speed
= 6*60/(160/3)
= 6 3/4 secs

I am not sure about the last calculation part of Relative Time. Can someone please cross-check the logic and the calculation of my explanation here?

I think your avg velocity formula can't be applied in this condition.
2ab/(a+b) is that same Distance different speed but here same time

Posted from my mobile device
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Re: Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
EDDIE98 wrote:
PRAGATIOSTWAL wrote:
I think the answer should be C.

Statement 1: NOT SUFFICIENT. Assuming the speed of the wheel A= x and B=3x, we cannot determine the individual actual speeds (which are required to answer this question).

Statement 2: NOT SUFFICIENT. The average speed also doesn't help to determine the individual actual speeds (which are required to answer this question).

Putting Statement 1 and Statement 2 together
The individual speeds can be determined by the formula: Average Speed= 2*S1*S2/(S1+S2)
40= 2*x*3x/(x+3x)
x= 80/3 revolutions per min (Speed of A)
3x= 80 revolutions per min(Speed of B)

Relative Distance= 6 rotations (given in the question stem)
Relative Speed= 80-80/3 revolutions per min (calculated above)

Time= Relative Distance/Relative Speed
= 6*60/(160/3)
= 6 3/4 secs

I am not sure about the last calculation part of Relative Time. Can someone please cross-check the logic and the calculation of my explanation here?

I think your avg velocity formula can't be applied in this condition.
2ab/(a+b) is that same Distance different speed but here same time

Posted from my mobile device

­Thank you for pointing out my mistake. I have corrected my solution/explanation now.
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Re: Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
@Bunuel Can you please provide the OE for this question. I am a bit confused.
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Re: Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
@Bunuel, can you please provide the OE for this question. I am a bit confused.
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Re: Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
PRAGATIOSTWAL wrote:
EDDIE98 wrote:
PRAGATIOSTWAL wrote:
I think the answer should be C.

Statement 1: NOT SUFFICIENT. Assuming the speed of the wheel A= x and B=3x, we cannot determine the individual actual speeds (which are required to answer this question).

Statement 2: NOT SUFFICIENT. The average speed also doesn't help to determine the individual actual speeds (which are required to answer this question).

Putting Statement 1 and Statement 2 together
The individual speeds can be determined by the formula: Average Speed= 2*S1*S2/(S1+S2)
40= 2*x*3x/(x+3x)
x= 80/3 revolutions per min (Speed of A)
3x= 80 revolutions per min(Speed of B)

Relative Distance= 6 rotations (given in the question stem)
Relative Speed= 80-80/3 revolutions per min (calculated above)

Time= Relative Distance/Relative Speed
= 6*60/(160/3)
= 6 3/4 secs

I am not sure about the last calculation part of Relative Time. Can someone please cross-check the logic and the calculation of my explanation here?

I think your avg velocity formula can't be applied in this condition.
2ab/(a+b) is that same Distance different speed but here same time

Posted from my mobile device

­Thank you for pointing out my mistake. I have corrected my solution/explanation now.

­I am sorry. I do not understand how you are calculating Average Speed. Why are we doing 2*S1*S2/(S1+S2) instead of your earlier way. I don't understand EDDIE's explanation. Same time but different distance covered so different speed right?
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Re: Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
OokandGluk: Here's the concept with which we proceeded to calculate Time in this question stem:
Case 1 – When the distance is constant: Average speed = 2xy/x+y; where x and y are the two speeds at which the same distance has been covered.
Case 2 – When the time taken is constant: Average speed = (x + y)/2; where x and y are the two speeds at which we traveled for the same time.

If you re-read the question requirement, it clearly states that we need to find time (in seconds) when the rotation of Wheel B is more than Wheel A. This means the distance traveled would differ for both wheels within the same time frame. Hence, we'll go with case 2 to calculate the speeds.
Re: Two bicycle wheels, A and B, start rotating at constant speeds at the [#permalink]
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