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

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02 Jun 2012, 21:43

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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?

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16 Jul 2013, 16:24

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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

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]

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25 Sep 2013, 22:33

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

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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]

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

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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]

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12 Dec 2014, 21:00

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

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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
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