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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
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Re: Circular gears P and Q start rotating at the same time at [#permalink]

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16 Mar 2017, 06:39
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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Re: Circular gears P and Q start rotating at the same time at [#permalink]

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21 Mar 2017, 06:24
Expert's post
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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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Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Mar 2017, 11:05
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: 23
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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18 Jul 2017, 17:59
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: 40
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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16 Aug 2017, 09:38
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..
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Re: Circular gears P and Q start rotating at the same time at [#permalink]

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13 Nov 2017, 17:10
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!!!
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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, 18:41
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
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Joined: 19 Aug 2016
Posts: 76
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Nov 2017, 19:24
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: 45257
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Nov 2017, 20:06
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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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, 03:14
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?
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Re: Circular gears P and Q start rotating at the same time at [#permalink]

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28 Feb 2018, 22:23
1
KUDOS
Expert's post
Hi All,

Once you convert each rate into revolutions/second, TESTing THE ANSWERS is a remarkably easy way to get to the correct answer. Algebraically, you can treat it as a "combined rate" question though:

Distance = (Rate) x (Time)

6 revolutions = (difference in rates) x (Time)

6 revolutions = (30 revolutions/min) x (Time)

6/30 = Time in minutes

1/5 minute = Time

Since the question asks for an answer in SECONDS, we have to convert....

1/5 minute = 12 seconds

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Re: Circular gears P and Q start rotating at the same time at [#permalink]

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15 Mar 2018, 22:53
Well, would like to understand if my approach is correct:
Gear P= 10/60 r/s = 1/6 r/s; Gear Q = 40/60 r/s = 2/3 r/s
difference between faster & slower gears = 2/3-1/6 = 1/2 r/s = .5 r/s
Now if gear Q gains .5 r in a second, it will require 2 seconds to gain 1 rev.
Therefore, 2 seconds/rev x 6 revs = 12 seconds.
Intern
Joined: 14 Feb 2016
Posts: 37
Re: Circular gears P and Q start rotating at the same time at [#permalink]

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18 Apr 2018, 09:17
Review:

See this is as a classical relative rates problem – applying the formula RT = D.

- In order to bridge the distance between the two gears, we take the rate of the faster gear and subtract that with the slower gear.

Rp: 10/60 = 1/6. Rq = 10/60 = 1/4.

- The question asks us – when will Q have made exactly 6 more revolutions than gear P?

Rq – Rp = 3/6 = 1/2 .

1/2 is the rate at which Q makes more revolutions then P. So when will gear Q have made exactly 6 more revolutions than gear P?

- 1/2 * T = 6
- T = 6*2 = 12.

12 seconds. Remember to convert minutes into seconds prior to playing with the formulas; as they ask for how many seconds after the gears start rotating….
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Re: Circular gears P and Q start rotating at the same time at   [#permalink] 18 Apr 2018, 09:17

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