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Circular gears P and Q start rotating at the same time at

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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   29 Sep 2020, 09:01
Look at it from a per unit perspective. Good Luck.
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   19 Oct 2020, 21:07
wfmd wrote:
My approach was the following (similar to what LalaB wrote):

Difference between gears Q and P is 30 revolutions per min (40-10).
To make 6 more rotations, the faster gear needs (6 rev / 30 rev/min = 1/5 min). Translate to seconds: 1/5 x 60 = 12.


I used this approach as well. Glad i'm not the only one
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Circular gears P and Q start rotating at the same time at [#permalink] New post   15 Nov 2020, 17:59
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Gear P makes 10 revolutions per minute

\(\frac{10 revolutions}{60 seconds} = \frac{ 1 revolution }{ 6 seconds}\)

Gear Q makes 40 revolutions per minute

\(\frac{40 revolutions}{60 seconds} = \frac{4 revolution }{ 6 seconds}\)

\(\frac{4x}{6} = \frac{x}{6} + 6\)
\(\frac{4x}{6} = x + \frac{36}{6}\)
\(4x = x + 36\)
\(3x = 36\)
\(x = 12\)

Answer is D.
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   17 Nov 2020, 19:55
Bunuel , this is a relatively easy question, but one thing that came to my mind:
Usually, we multiply the number of revolutions by 2pie. Why didn't we do it in this problem?

Thank you!
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   17 Nov 2020, 20:20
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HWPO wrote:
Bunuel , this is a relatively easy question, but one thing that came to my mind:
Usually, we multiply the number of revolutions by 2pie. Why didn't we do it in this problem?

Thank you!


Hi HWPO,

We might use the formula for Circumference (re: C = 2pi(r)) if we were calculating the 'distance traveled' by the rotating gears. Here though, we're not interested in that - we're interested in total revolutions (and since we have the two RATES that the gears are spinning, the actual radii of the gears - and thus, the circumference of the gears - is irrelevant to the calculation).

GMAT assassins aren't born, they're made,
Rich
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   17 Nov 2020, 20:47
EMPOWERgmatRichC wrote:
HWPO wrote:
Bunuel , this is a relatively easy question, but one thing that came to my mind:
Usually, we multiply the number of revolutions by 2pie. Why didn't we do it in this problem?

Thank you!


Hi HWPO,

We might use the formula for Circumference (re: C = 2pi(r)) if we were calculating the 'distance traveled' by the rotating gears. Here though, we're not interested in that - we're interested in total revolutions (and since we have the two RATES that the gears are spinning, the actual radii of the gears - and thus, the circumference of the gears - is irrelevant to the calculation).

GMAT assassins aren't born, they're made,
Rich


Makes perfect sense. Thank you, Rich
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   11 Jan 2021, 09:01
Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?


Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let \(t\) be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

Hope it's clear.



Hey! I have tried to explain to myself in wording the logic of the function but was never able to really comprehend why the +6 is added to T and not Q in the created function.
I understand that we look for a point in time where t in both gears is equal but revolutions +6 for Q, so why 6 were added to P instead?
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Circular gears P and Q start rotating at the same time at [#permalink] New post   21 Mar 2021, 00:47
Q rotates 4x as fast as P. Therefore:

Q - - - - - - P
1 rev --> 1/4 rev
4 rev --> 1 rev ==> at this stage Q has 3 more rotations than P. We want 6 more (double the current difference), so;
8 rev --> 2 rev ==> at this stage Q has 6 more rotations than P. So we need to find t for when either Q has completed 8 revolutions or P has completed 2 revolutions

For Q:
40rev --> 1 min
8 rev --> 8/40 = 1/5 min = 12s

(For P: 10 rev --> 1 min, 2 rev --> 2/10 = 1/5 min = 12s)
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   25 May 2021, 20:19
P = 10 rev/ min = 10 rev in 60 seconds ( 1 min = 60 sec)

Q = 40 rev/ min = 40 rev in 60 sec ( 1 min = 60 sec)

Difference Q-P = 30 rev ( 40 -10) in 60 sec


Ratio of difference in rev : time 30 rev : 60 sec
1 rev : 2 sec

For differenceof 6 rev 6rev : 12 sec
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   21 Jan 2023, 14:18
enigma123 wrote:
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15


Hi BrentGMATPrepNow, in conversion of min > second, noticed that some experts here calcuate it as min/60 but some as min * 60 and still arrive at the same answer. Why is that and could you help?

10/60t+6=40/60t --> t=12s.

OR > (40-10) t = 6
t= 1/5 min * 60 > t = 12s
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Circular gears P and Q start rotating at the same time at [#permalink] New post   23 Jan 2023, 13:55
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Kimberly77 wrote:
enigma123 wrote:
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15


Hi BrentGMATPrepNow, in conversion of min > second, noticed that some experts here calculate it as min/60 but some as min * 60 and still arrive at the same answer. Why is that and could you help?

10/60t+6=40/60t --> t=12s.

OR > (40-10) t = 6
t= 1/5 min * 60 > t = 12s


The formulas seconds = minutes/60 and seconds = minutes * 60 are not both correct.

We can quickly test this by plugging in a certain number of minutes.
For example, let's plug in 2 minutes.
For each "formula," we get:

seconds = minutes/60
seconds = 2/60 = 1/30
So, using this formula, 2 minutes = 1/30 seconds.

seconds = minutes * 60
seconds = 2 * 60 = 120
So, using this formula, 2 minutes = 120 seconds.

As you can see, the first formula does not work
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post   13 Feb 2024, 11:41
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Re: Circular gears P and Q start rotating at the same time at [#permalink]
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