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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] New post 20 Mar 2012, 09:04
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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] New post 20 Mar 2012, 09:11
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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.

Answer: D.

Hope it's clear.
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 01 Jul 2012, 03:55
(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] New post 18 Apr 2013, 09:28
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
Re: Circular gears P and Q start rotating at the same time at   [#permalink] 18 Apr 2013, 09:28
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