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
I understand for this problem that P rate = 10/1 (in minutes) and 1/6 (in seconds, and that Q = 40/1 (in minutes) and 2/3 (in seconds). You can write out up to 12 steps counting to see when they are 6 rotations apart, but what is the algebraic expression to solve this?
Would it be 1/6x = 2/3x + 6
1/6x - 2/3x = 6
- 3/6x =6
x = -12
Work Problem
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi melanie.espeland,
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
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
When elements COMPETE, determine the DIFFERENCE between the rates.melanie.espeland 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
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.
Other problems that can be 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
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I like Mitch's approach a lot, but here's one more (longer) approach for your math toolbox:melanie.espeland 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
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
-
- Newbie | Next Rank: 10 Posts
- Posts: 1
- Joined: Sun Nov 23, 2014 12:10 am
Back solving...
we know gear P in one sec completes 1/6 rev and gear Q 2/3 rev.
starting from choice D which is multiple of factors in both fractions, P would have completed 2 revs and Q 8 revs. The difference is Q-P =6.
we know gear P in one sec completes 1/6 rev and gear Q 2/3 rev.
starting from choice D which is multiple of factors in both fractions, P would have completed 2 revs and Q 8 revs. The difference is Q-P =6.
-
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
Comparing ratios is very simple -
P:Q:difference
1:4:3
2:8:6
2 revolutions takes 2/10 minutes = 12 seconds
P:Q:difference
1:4:3
2:8:6
2 revolutions takes 2/10 minutes = 12 seconds
-
- Senior | Next Rank: 100 Posts
- Posts: 94
- Joined: Tue Dec 16, 2014 9:50 am
- Location: London, UK
- Thanked: 2 times
- Followed by:4 members
- GMAT Score:770
Relative speed: Q rotates 30 revolutions more per minute (60 seconds) that P.
To find out how long it takes Q to do 6 more revolutions than P we simply need to multiply 60 seconds by 1/5 (which is obtained by dividing 6/30).
Answer: 12 seconds.
To find out how long it takes Q to do 6 more revolutions than P we simply need to multiply 60 seconds by 1/5 (which is obtained by dividing 6/30).
Answer: 12 seconds.