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

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Circular gears P and Q start rotating at the same time at [#permalink]  20 Mar 2012, 08:04
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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
[Reveal] Spoiler: OA

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Re: Circular Gears [#permalink]  20 Mar 2012, 08:11
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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.
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  01 Jul 2012, 02:55
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(40-10)*t=6

t=1/5 mins

(1/5)*60=12 sec
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  18 Apr 2013, 08:28
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I used the following approach:

Circular P has 10rpm >> Therefore one rotation will be every 10/60 seconds

Circular Q has 40rpm >> Therefore one rotation will be every 40/60 seconds

Now we are asked after how many seconds will circular Q have made 6 more rotations than Circular P. Translating into algebra

4/6S-1/6(S)=6

Solve for S (where s is number of seconds)
S=12
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  25 Oct 2013, 22:48
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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

Work done by Faster gear Q is 6 more than slower gear P in same time

i.e W(q) = W(p) + 6
Rq X t = Rp X t + 6
40t=10t + 6
30t = 6
t =1/5 hrs
t = 12 mins
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Re: Circular Gears [#permalink]  21 Nov 2013, 00:54
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.

Is there any theory for this?

I remember from college days, the Key point in solving is that the tangential Velocity should be same at the point of contact?
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  21 Nov 2013, 01:42
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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.
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  26 Jan 2014, 22:25
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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

All the above answers are excellent and I would like to one little tweak that has helped me in quite a few number of Quant problems. This is applicable for people who love to find answers by plugging in the options given

As soon as you arrive at the 2 numbers "6 seconds and 1.5 seconds" (Time taken to complete one rotation) , look at the options given. The best options(9 out of 10 times) are the ones that are a multiple of the above two numbers. Hence you will possibly start with option A and then move to option B and voila.

NOTE: Use this method in scenarios such as this example wherein the number of options that fall under the "multiple umbrella"are quite low. If all the options are multiples it is better to switch on to one of the above strategies.
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  22 Jul 2014, 10:33
----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
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  30 Aug 2014, 23:23
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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

Another approach: P makes 10 R(evolutions) in 60 secs, so 1 R in 6 Sec. Similarly, as Q makes 40 R in 60 Sec or 4 R in 6 Sec. We can extrapolate the above details to state that P would make 2 R in 12 Sec and Q would make 8 R in 12 sec. Hence Q needs additional 12 Sec to overtake P by 6 Revolutions.
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  09 Jun 2015, 09:44
This problem is present in both difficulty level
Sub 600 and 600-700
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Re: Circular gears P and Q start rotating at the same time at [#permalink]  10 Jun 2015, 09:53
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We can resolve this by as following

Gear P

Speed of gear P per second = 10revolutions/60 secs
=1/6 revolutions per second

Speed of gear Q per second = 40revolutions/60 secs
=4/6 revolutions per second

Distance travelled P Q
1sec 1/6 revolutions 4/6 revolutions
6 sec 1 revolution 4 revolution
12 sec 2 revolution 8 revolutions

Hence in 12 seconds Gear P completes 2 rev and Gear Q completes 8 rev
Difference =8-2= 6 revolutions
Therefore in 12 sec Gear Q revolves 6 times ahead than Gear P

Hope this makes it
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Re: Circular gears P and Q start rotating at the same time at   [#permalink] 10 Jun 2015, 09:53
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