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

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Director
Joined: 12 Nov 2016
Posts: 790
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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16 Mar 2017, 05:39
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 --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Hope it's clear.

It's definitely clear- I even reduced it to 10/60t +6=40/60t to 1/6t + 6 = 4/6t in order to make it more manageable- though if we can think quick enough it might help to use different variables like x since "t" under timed pressure can look like a plus sign and create stress- at least small things like those are what happened on my first GMAT and caused major blank outs.
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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21 Mar 2017, 05:24
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

As we can see, Gear Q makes 30 more revolutions per minute than Gear P does. So, we can set up the following proportion to solve for the number of seconds for Gear Q to make 6 more revolutions than Gear P does:

30 revolutions/1 minute = 6 revolutions/x seconds

We need the units of time to be the same in the denominator. Since 1 minute = 60 seconds, we can say:

30/60 = 6/x

Cross multiply and we have:

30x = 360

x = 12

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Manager
Joined: 03 Jan 2017
Posts: 193
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Mar 2017, 10:05
let's translate into seconds:
P: 1/6 per second
Q: 2/3 per second
we can make the following equation: P*S=Q*S-6
6=s(q-p)
6=s*1/2
s=12
Intern
Joined: 14 May 2016
Posts: 12
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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18 Jul 2017, 16:59
Here is how I solved it:

Gear P

10 * 1 min/60 sec = 10/60 or 1/6

Gear Q

40 * 1 min/60 = 40/60 or 4/6

Now let's do ratios:

P Q
1/6 : 4/6

2/6 : 5/6

3/6 : 6/6

now lets cross multiply
P Q
3/6 * 4/6 = 12/6

Joined: 30 May 2015
Posts: 39
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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16 Aug 2017, 08:38
very easy if you apply relative speed concept
Relative speed of P & Q is 30 RPM
so 30 Revolution in 60 sec
then 6 revolution will take 12 second Ans..
Intern
Joined: 24 Jan 2017
Posts: 9
Location: Brazil
Concentration: Strategy, Entrepreneurship
GPA: 3.5
WE: Consulting (Consulting)
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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13 Nov 2017, 16:10
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 --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Hope it's clear.

Bunuel

I did this exercise using relative velocity:

P=> 10rev/60sec / Q=> 40rev/60sec / Vrel= 30rev/60sec or Vrel= 1rev/2sec Ω
So, 6 revolutions will take 12 seconds

Does it make sense? Or it was a lucky guess?!

TKS!!!
Manager
Joined: 13 Jun 2012
Posts: 185
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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13 Nov 2017, 17:41
1
KUDOS
GuilhermeAzevedo wrote:
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 --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Hope it's clear.

Bunuel

I did this exercise using relative velocity:

P=> 10rev/60sec / Q=> 40rev/60sec / Vrel= 30rev/60sec or Vrel= 1rev/2sec Ω
So, 6 revolutions will take 12 seconds

Does it make sense? Or it was a lucky guess?!

TKS!!!

Sorry not Bunnel, but I did it in the same way. Also, below is a method.

10T+6=40T ; 30T=6; T=1/5. now we have to convert it sec. so 1/5*60= 12
Manager
Joined: 19 Aug 2016
Posts: 72
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Nov 2017, 18:24
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 --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Hope it's clear.

Hi Bunuel,

How did u arrive at (10/60)t?

then time is t

are we calculating the distance here? Could u pls explain the logic to me?

Math Expert
Joined: 02 Sep 2009
Posts: 43867
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Nov 2017, 19:06
zanaik89 wrote:
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 --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Hope it's clear.

Hi Bunuel,

How did u arrive at (10/60)t?

then time is t

are we calculating the distance here? Could u pls explain the logic to me?

10/60 is the number of revolutions per second and t is the time in seconds. What would you get when you multiply those two? (revolutions per second)(time in seconds) = ?
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Intern
Joined: 01 Dec 2017
Posts: 2
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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17 Jan 2018, 02:14
The rates of the two gears have a ratio of 4:1.
The question asks for +6 seconds.
My thought was, that the only number of the answers which has factors 4, 6 and 1 is 12. The solving process took me therefore only about 10 seconds. BUT I wonder if this is a possible approach or if this is just an example of luck?
Re: Circular gears P and Q start rotating at the same time at   [#permalink] 17 Jan 2018, 02:14

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