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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]

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New post 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 --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

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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New post 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

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

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New post 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
Answer is D
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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New post 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

hence answer is 12
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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

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New post 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 --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

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

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New post 13 Nov 2017, 17:41
1
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 --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

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

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New post 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 --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

Hope it's clear.


Hi Bunuel,

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

when speed is already 10/60

then time is t

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

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

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New post 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 --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

Hope it's clear.


Hi Bunuel,

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

when speed is already 10/60

then time is t

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

Thanks in advance


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

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New post 17 Jan 2018, 02:14
I thought about this problem in another way and wonder if this is also possible:
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?
Thank you for your answers!
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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New post 28 Feb 2018, 21:23
1
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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New post 15 Mar 2018, 21:53
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.
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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New post 18 Apr 2018, 08:17
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]

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New post 10 Sep 2018, 18:41
Bunuel, can you share more such questions ?
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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New post 10 Sep 2018, 20:30
ammuseeru wrote:
Bunuel, can you share more such questions ?


Sure.

Similar questions to practice:
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Hope it helps.
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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New post 16 Oct 2018, 00:55
Its relative speed concept here..

Note we can imagine distance in terms of revolutions here and its better to convert rev/min to rev/sec since answer is in seconds unit.

Now,

P speed= 10rev/min= 10/60 rev/sec=1/6 rev/sec
Q speed = 40 rev/min = 40/60 = 2/3 rev/sec

Now we need to make up for 6 revolutions an relative speed is 2/3-1/6=1/2 rev/sec

There time taken to cover 6 rev = 6 /(1/2) = 12 seconds




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

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New post 13 Feb 2019, 05:53
----RATE-----time--------distance
P:---10 -----x/10------------ x
Q:---40------(x+6)/40-------x+6

The time should be equal, so we solve x/10 = (x+6)/40
x=2

so time = 2/10 min = 12 sec

Can anyone explain me how we get from x=2 ----> to 12 sec???
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Re: Circular gears P and Q start rotating at the same time at  [#permalink]

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New post 13 Feb 2019, 18:54
Hi hsn81960,

You did not label the "units" in your table, but based on the work that you presented, I think that you know that time is in MINUTES.

You solved for X and got X=2... when you plug that back in for X you get:

2/10 = 1/5 of a minute for Gear P
8/40 = 1/5 of a minute for Gear Q

Thus, it clearly takes 1/5 of a 1 minute for the revolutions to match what the question asked for. Since 1 minute = 60 seconds, then (1/5)(60) = 12 seconds

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Re: Circular gears P and Q start rotating at the same time at   [#permalink] 13 Feb 2019, 18:54

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