P and Q Circular gears rate problem... can I do it this way?

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benjiboo: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members; Location: NYC; Thanked: 33 times; GMAT Score:710

by benjiboo » Mon Sep 17, 2012 8:39 pm

thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

See attached picture: Can I say that one does "P does "S" spins and Q does "S + 6" spins", then figure out the time and set equal as shown?

Is this wrong and I just got lucky, or is this actually the right approach?

Secondly, can I say:

Combined rate is 1/2, therefore to do six extra spins, it would be 6/1/2 = 12?

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Source: Beat The GMAT — Problem Solving | Mon Sep 17, 2012 8:39 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 17, 2012 9:03 pm

benjiboo wrote:thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

See attached picture: Can I say that one does "P does "S" spins and Q does "S + 6" spins", then figure out the time and set equal as shown?

Is this wrong and I just got lucky, or is this actually the right approach?

Secondly, can I say:

Combined rate is 1/2, therefore to do six extra spins, it would be 6/1/2 = 12?

I think your approach looks good, but I'm not 100% certain what some of your numbers and expressions represent. Can you offer a little more rationale.

In the meantime, here's one possible approach:

First rewrite speeds as revolutions per second (since the question uses these units)

Gear P makes 10 revolution per minute, in other words 10 revolutions per 60 seconds.
To determine the number of revolutions per 1 second, divide 10 by 60, to get 10/60 revolutions per second (a.k.a. 1/6 revolutions per second)

Gear Q makes 40 revolution per minute (or 40 revolutions per 60 seconds).
To determine the number of revolutions per 1 second, divide 40 by 60, to get 40/60 revolutions per second (a.k.a. 2/3 revolutions per second)

Now let t = the time in seconds

The number of revolutions gear P makes in t seconds = (1/6)t
The number of revolutions gear Q makes in t seconds = (2/3)t

We need to determine the number of seconds it takes such that gear Q makes exactly 6 more revolutions than gear P.

So, we want to know the value of t such that:
(Q's revolutions) - (P's revolutions) = 6
Or . . . (2/3)t - (1/6)t = 6
To solve, first multiply both sides by 6 to get: 4t - t = 36
3t = 36
t = 12

It will take 12 seconds, so the answer is D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Newbie_FastLearner: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Jul 12, 2012 9:40 amFollowed by: 1 member

by Newbie_FastLearner » Mon Sep 17, 2012 10:50 pm

Brent@GMATPrepNow wrote:
benjiboo wrote:thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

See attached picture: Can I say that one does "P does "S" spins and Q does "S + 6" spins", then figure out the time and set equal as shown?

Is this wrong and I just got lucky, or is this actually the right approach?

Secondly, can I say:

Combined rate is 1/2, therefore to do six extra spins, it would be 6/1/2 = 12?
I think your approach looks good, but I'm not 100% certain what some of your numbers and expressions represent. Can you offer a little more rationale.

In the meantime, here's one possible approach:

First rewrite speeds as revolutions per second (since the question uses these units)

Gear P makes 10 revolution per minute, in other words 10 revolutions per 60 seconds.
To determine the number of revolutions per 1 second, divide 10 by 60, to get 10/60 revolutions per second (a.k.a. 1/6 revolutions per second)

Gear Q makes 40 revolution per minute (or 40 revolutions per 60 seconds).
To determine the number of revolutions per 1 second, divide 40 by 60, to get 40/60 revolutions per second (a.k.a. 2/3 revolutions per second)

Now let t = the time in seconds

The number of revolutions gear P makes in t seconds = (1/6)t
The number of revolutions gear Q makes in t seconds = (2/3)t

We need to determine the number of seconds it takes such that gear Q makes exactly 6 more revolutions than gear P.

So, we want to know the value of t such that:
(Q's revolutions) - (P's revolutions) = 6
Or . . . (2/3)t - (1/6)t = 6
To solve, first multiply both sides by 6 to get: 4t - t = 36
3t = 36
t = 12

It will take 12 seconds, so the answer is D

Cheers,
Brent

Relative Speed of Q wrt P = 30 revolution per minute-> Q makes 1\2 revolution per second. This follows, to make 6 revolution extra, Q has to take 12 seconds.

Brent is this approach correct??

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Sep 18, 2012 4:59 am

benjiboo wrote:thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

When elements COMPETE, determine the DIFFERENCE between the rates.
Q's rate - P's rate = 40-10 = 30 revolutions per minute.
Time for Q to make 6 more revolutions = (number of revolutions)/(rate difference) = 6/30 = 1/5 of a minute = 12 seconds.

The correct answer is D.

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benjiboo: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members; Location: NYC; Thanked: 33 times; GMAT Score:710

by benjiboo » Tue Sep 18, 2012 9:55 am

GMATGuruNY wrote:
When elements COMPETE, determine the DIFFERENCE between the rates.
Q's rate - P's rate = 40-10 = 30 revolutions per minute.
Time for Q to make 6 more revolutions = (number of revolutions)/(rate difference) = 6/30 = 1/5 of a minute = 12 seconds.

The correct answer is D.

Is this always true? So the time it takes "Train A" to go 10 more miles than "Train B" if "the difference between their rates is 5mph" is simply 10/5 = 2 hours?

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benjiboo: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members; Location: NYC; Thanked: 33 times; GMAT Score:710

by benjiboo » Tue Sep 18, 2012 9:56 am

Brent@GMATPrepNow wrote:
I think your approach looks good, but I'm not 100% certain what some of your numbers and expressions represent. Can you offer a little more rationale.

In the meantime, here's one possible approach:

First rewrite speeds as revolutions per second (since the question uses these units)

Gear P makes 10 revolution per minute, in other words 10 revolutions per 60 seconds.
To determine the number of revolutions per 1 second, divide 10 by 60, to get 10/60 revolutions per second (a.k.a. 1/6 revolutions per second)

Gear Q makes 40 revolution per minute (or 40 revolutions per 60 seconds).
To determine the number of revolutions per 1 second, divide 40 by 60, to get 40/60 revolutions per second (a.k.a. 2/3 revolutions per second)

Now let t = the time in seconds

The number of revolutions gear P makes in t seconds = (1/6)t
The number of revolutions gear Q makes in t seconds = (2/3)t

We need to determine the number of seconds it takes such that gear Q makes exactly 6 more revolutions than gear P.

So, we want to know the value of t such that:
(Q's revolutions) - (P's revolutions) = 6
Or . . . (2/3)t - (1/6)t = 6
To solve, first multiply both sides by 6 to get: 4t - t = 36
3t = 36
t = 12

It will take 12 seconds, so the answer is D

Cheers,
Brent

Brent,

S= # of spins.

In my photo, filled in the middle column last - by using the right column, and the given rates.

Does this make sense now?

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 19, 2012 6:23 am

benjiboo wrote: Brent,

S= # of spins.

In my photo, filled in the middle column last - by using the right column, and the given rates.

Does this make sense now?

Ah, yes it does!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 20, 2012 4:02 am

benjiboo wrote:
GMATGuruNY wrote:
When elements COMPETE, determine the DIFFERENCE between the rates.
Q's rate - P's rate = 40-10 = 30 revolutions per minute.
Time for Q to make 6 more revolutions = (number of revolutions)/(rate difference) = 6/30 = 1/5 of a minute = 12 seconds.

The correct answer is D.
Is this always true? So the time it takes "Train A" to go 10 more miles than "Train B" if "the difference between their rates is 5mph" is simply 10/5 = 2 hours?

Correct! Some other problems that I solved by determining the CATCH-UP rate:

https://www.beatthegmat.com/rates-work-t119850.html
https://www.beatthegmat.com/dune-buggie-t108778.html
https://www.beatthegmat.com/interesting- ... 16571.html
https://www.beatthegmat.com/rate-problem-t111575.html

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