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Circular gears L and R start to rotate at the same time at the same ra

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Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 08 Aug 2010, 18:23
19
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A
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D
E

Difficulty:

  25% (medium)

Question Stats:

78% (02:11) correct 22% (02:35) wrong based on 255 sessions

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Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 10 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

a) 6
b) 8
c) 10
d) 12
e) 15
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 08 Aug 2010, 18:58
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2
Gear L -- 10 rotations per 60 seconds -- 1 rotation per 6 seconds.
Gear R -- 40 rotations per 60 seconds -- 4 rotations per 6 seconds.

First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 3 rotations

Hence every 6 seconds the difference between the number of rotations of R and L gear is 3 units.

Required net difference should be 6 rotations => 2 (6 seconds later) ==> 12 seconds.

Answer: 12 seconds (Option D).
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 08 Aug 2010, 18:52
2
My approach:

Gear L: 10 rev in 60 sec => 1/6 rev in 1 sec

Gear R: 40 rev in 60 sec => 2/3 rev in 1 sec

Difference in 1 sec = 2/3 -1/6 = 1/2 rev in 1 sec.

i.e it takes 1 sec for a difference of 1/2 revolutions between the gears.

it takes 2 secs for a difference of 1 complete revolution

hence 2X6 = 12 secs for difference of 6 complete revolutions.

Hope this is ok!!!
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 09 Aug 2010, 09:45
this is excellent quetion for backsolving....
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Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post Updated on: 16 Aug 2016, 20:28
let m=# min
m*(40-10 rpm)=6 rev
m=6/30=1/5 min=12 sec

Originally posted by gracie on 16 Aug 2016, 14:16.
Last edited by gracie on 16 Aug 2016, 20:28, edited 1 time in total.
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 16 Aug 2016, 18:20
L = 10 rev/min = (10/60) rev/sec = (1/6) rev/sec
R = 40 rev/min = (40/60) rev/sec = (2/3) rev/sec

L in 1 sec makes (1/6) revolutions
L in 2 sec makes (1/6)*2=(1/3) revolutions
L in 3 sec makes (1/6)*3=(1/2) revolutions

R in 1 sec makes (2/3) revolutions
R in 2 sec makes (2/3)*2=(4/3) revolutions
R in 3 sec makes (2/3)*3=(2) revolutions

x = seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L
(2/3)*x=(1/6)*x + 6
(4/6-1/6)*x=6
(1/2)*x=6
x=12 seconds
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 22 Sep 2016, 03:50
My approach:

Take x to be the number of minutes after which Gear R would have made 6 more revolutions than Gear L:

10x+6=40x
6=30x
6/30=x
--------
6/30 is in minutes, to convert into seconds we multiply by 60
Therefore, 6/30 X 60, which equals 12 seconds.
Although this isn't the "rate and work" way to go, I thought this was quicker.
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 13 Jul 2018, 13:17
1
Yalephd wrote:
Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 10 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

a) 6
b) 8
c) 10
d) 12
e) 15


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

30 revolutions/1 minute = 6 revolutions/x seconds

We need for both denominators to have the same units. Since 1 minute = 60 seconds, we can re-express the proportion as:

30/60 = 6/x

Cross multiplying, we have:

30x = 360

x = 12

Alternate Solution:

Gear L makes one revolution in 60/10 = 6 seconds and gear R makes one revolution in 60/40 = 1.5 seconds. If we let n the time (in seconds) that passes when gear R makes 6 more revolutions than gear L, we can create the following equation:

n/1.5 - n/6 = 6

Let’s multiply each side by 6:

4n - n = 36

3n = 36

n = 12

Answer: D
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 26 Jul 2018, 05:20
Gear R makes 30 more revolution per minute than gear L, or, 1/2 revolution per second (30/60).
Lets say that X is the seconds needed to gear R to be exactly 6 revolutions ahead.

1/2*X = 6
X = 6 / 1/2
X = 6 * 2
X = 12

Option D.
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 18 Jan 2020, 12:58
L = 10 Rev/min
R = 40 Rev/min
R/L = 4 ; R = 4 L
How many second, R has made exactly 6 more revolutions than gear L
Needed R = L+6 ; 4L=L+6 ; 3L=6; L=2.
Since L does 10 Rev in 1 min. It will do 2 Rev in 60/5 = 12 seconds.
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Re: Circular gears L and R start to rotate at the same time at the same ra  [#permalink]

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New post 19 Jan 2020, 02:48
1
Relative Speed = 40-10 = 30 rev per minute
Distance = 6 revs
Time = distance/relative speed= 6/30 = 0.2 minutes
Time in seconds = 0.2 x 60= 12 seconds
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Re: Circular gears L and R start to rotate at the same time at the same ra   [#permalink] 19 Jan 2020, 02:48
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