Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

02 Jun 2012, 21:43

1

This post received KUDOS

15

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

69% (02:55) correct
31% (02:22) wrong based on 403 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?

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.

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

12 Jul 2012, 01:51

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.

The 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.

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

16 Jul 2013, 16:24

5

This post received KUDOS

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

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

25 Sep 2013, 22:33

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 _____________________________________________________________________________

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

27 Nov 2013, 03:42

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.
_________________

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

12 Dec 2013, 11:53

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.

Re: Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

12 Dec 2014, 21:00

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.
_________________

Two wheels are connected via a conveyor belt. The larger [#permalink]

Show Tags

02 May 2016, 07:54

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

gmatclubot

Two wheels are connected via a conveyor belt. The larger
[#permalink]
02 May 2016, 07:54

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...