Author 
Message 
TAGS:

Hide Tags

Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 395
Location: Canada
GMAT 1: 620 Q42 V33 GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)

Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
02 Jun 2012, 22:43
1
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
69% (02:53) correct
31% (02:20) wrong based on 427 sessions
HideShow timer Statistics
Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r? A. 1280π B. 75r C. 48r D. 24r E. (64π)/3
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Joined: 17 Dec 2012
Posts: 550
Location: India

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
16 Jul 2013, 17:24
5
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
macjas wrote: Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
A. 1280π B. 75r C. 48r D. 24r E. (64π)/3 1. Let the number of revolutions made by the smaller wheel in 1 hr be s 2. Given: Number of centimeters rotated by both the wheels in 1 hr is the same 3. Number of centimeters rotated by the larger wheel in one revolution = its circumference=2*pi*20=40Pi 4. Number of centimeters rotated by the larger wheel in 1 hr = 40*pi*60*r 5. Number of centimeters rotated by the smaller wheel in one revolution=its circumference=2*pi*16=32*pi 6.Number of centimeters rotated by the smaller wheel in 1 hr= 32*pi*s 7. Equating (4) and (6) based on (2), 40*pi*60*r = 32*pi*s i.e., s= 75r
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com
Classroom and Online Coaching



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
03 Jun 2012, 03:16
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
macjas wrote: Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
A. 1280π B. 75r C. 48r D. 24r E. (64π)/3 The radius of the larger wheel is 20cm so, its circumference is \(2\pi{R}=40\pi\). Since the larger wheel makes r revolution per minute or 60r revolutions per hour then it rotates \(60r*40\pi\) centimeters per hour. The radius of the smaller wheel is 16cm so, its circumference is \(2\pi{R'}=32\pi\). Now, in order the smaller wheel to rotate the same centimeters per time interval it should make \(\frac{60r*40\pi}{32\pi}=75r\) revolutions per hour. Answer: B.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 03 Aug 2012
Posts: 893
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
25 Sep 2013, 23:33
1
This post received KUDOS
Visualization is the key in such problems. To work smoothly The belt left by big wheel should be taken up by small wheel. Implicitly, Length left by big wheel /min = length accepted by small wheel/min 40 *pi * r = 32 * pi * x x = (5/4) * r in minute x= (5/4) * r * 60 in hour Hence B
_________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________



Current Student
Joined: 18 Mar 2011
Posts: 45

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
11 Jul 2012, 10:39
Hai guys..
I just tried this way..
40P/no of centimeters = R per minute
So no of centi = 40P/R
since both the wheels move at the same rate i.e in terms of centi Revol for the smaller one = 32P*R/40P =4/5R per minute and 48R per hour...
What am I missing ?



Intern
Joined: 08 May 2012
Posts: 4

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
12 Jul 2012, 02:51
My take on it, the wheel will cover PI*40 cm in one rotation. Thus to if we know total distance in a unit time, the expression for rev. should be No of centi per minute/PI*40 = rev per minute Also as if you look at the unit at both side LHS: no of cm per minute => units are cm/min PI*40 => units are cm RHS Rev per minute => units are (min)^1 or (1/min) Thus, [cm/min] /[cm] = [1/min] showing the equation balances and in your case you inverted the LHS of the equation. Rest is you can equate the total distance for both wheel PI*32*R = PI*40 *r R = 5/4*r in cm/m or 5/4*r*60 = 75*r cm/h.



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
12 Jul 2012, 03:15
Priyanka2011 wrote: Hai guys..
I just tried this way..
40P/no of centimeters = R per minute
So no of centi = 40P/R
since both the wheels move at the same rate i.e in terms of centi Revol for the smaller one = 32P*R/40P =4/5R per minute and 48R per hour...
What am I missing ? Check this: twowheelsareconnectedviaaconveyorbeltthelarger133697.html#p1092048The circumference of the larger wheel is \(2\pi{R}=40\pi\). Since the larger wheel makes \(r\) revolution per minute or \(60r\) revolutions per hour, then it rotates \(60r*40\pi\) centimeters per hour. The radius of the smaller wheel is 16cm so, its circumference is \(2\pi{R'}=32\pi\). Now, in order the smaller wheel to rotate the same centimeters per time interval it should make \(\frac{60r*40\pi}{32\pi}=75r\) revolutions per hour. Answer: B. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
16 Jul 2013, 00:14



Intern
Joined: 20 Jun 2013
Posts: 8

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
24 Jul 2013, 06:53
I just applied the values: r revolutions in 1 min, so 60r in 60mins. Consider a point on this wheel. In each revolution of the larger wheel, this point travels 40 cms, so at the end of 60r it travels 2400cms. How many revolutions will it take for a point on the smaller wheel to cover this distance? 2400/32 = 75r



Manager
Joined: 25 Oct 2013
Posts: 169

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
27 Nov 2013, 04:42
There is a simple formula for this kind of problems. Given two pulleys/wheels are connected tightly with a conveyor belt, each wheels completes same distance in an hour as the other wheel unless there is slippage. only their revolutions per min or hour differ due to their difference is size. If r1 and r2 are revolutions per hour of each wheel and R1 and R2 are radius of each wheel. equating distance of each wheel \(2pi*R1*r1 = 2pi*R2*r2\) \(R1*r1 = R2*r2\) \(\frac{R1}{R2} = \frac{r2}{r1}\) given 3 of the values we can find the 4th one.
_________________
Click on Kudos if you liked the post!
Practice makes Perfect.



Senior Manager
Joined: 13 May 2013
Posts: 469

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
12 Dec 2013, 12:53
Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
Interesting to note that the larger wheel has a diameter of 40 (8*5) while the smaller one has a diameter of 32 (8*4)...
If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 40pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.25 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.25 = 12.5 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.25 = 750 revolutions per hour.
If r = 10, then the answer choice must be b.
B. 75r



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15915

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
12 Dec 2014, 22:00
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Director
Joined: 07 Dec 2014
Posts: 706

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
06 Nov 2015, 10:16
large wheel does 60r rph small wheel does (40/32)(60r)=75r rph



Intern
Joined: 10 Aug 2015
Posts: 29
Location: India
GPA: 3.5
WE: Consulting (Computer Software)

Two wheels are connected via a conveyor belt. The larger [#permalink]
Show Tags
02 May 2016, 08:54
Priyanka2011 wrote: Hai guys..
I just tried this way..
40P/no of centimeters = R per minute
So no of centi = 40P/R
since both the wheels move at the same rate i.e in terms of centi Revol for the smaller one = 32P*R/40P =4/5R per minute and 48R per hour...
What am I missing ? Here is an alternate time saving solution with the use of ratios and also to clear doubt of friends who have similar question as above. Now the ratio of the wheels circumferences will be same as the ratio of their radii.(find out why ) Now R/r=40/32=5/4. Then the ratio of their speeds will be opposite to their ratio of time and ratio of the time taken = ratio of their radii if we keep distance constant. So we know that smaller circle will have a higher revolution speed than larger.Now c,d,e are out. Left only a and b. We can clearly see 1280pi will never be our answer. We can just select B and go ahead or we can do as stated below. Now we know revolution = r per min. So 60r/hr. So smaller wheel's rev=60r*(inversed ratio)= 60r*5/4= 75r




Two wheels are connected via a conveyor belt. The larger
[#permalink]
02 May 2016, 08:54







