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# A circular rim 28 inches in diameter rotates the same number

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A circular rim 28 inches in diameter rotates the same number [#permalink]

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08 Jun 2008, 11:01
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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Jan 2013, 06:39, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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08 Jun 2008, 13:17
I want to pick 48x, but choice B stands out from the rest, so B it is.

puma wrote:
A circular rim 28 inches in a diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes X revilutions per second, how many revilutions per minute does the larger rim makes in terms of X?

a) 48pi/x
b) 75m
c) 48x
d) 24x
e) x/75

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08 Jun 2008, 21:44
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puma wrote:
A circular rim 28 inches in a diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes X revilutions per second, how many revilutions per minute does the larger rim makes in terms of X?

a) 48pi/x
b) 75m
c) 48x
d) 24x
e) x/75

circumference * (rev/min) of 28 =circumference * (rev/min) of 35
to calculate z
pi*28*x=pi*35*z
z=4/5 * x
but this is inch/sec we want inch/min

z=4/5 * x*60
=48x

C

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30 Jul 2009, 13:44
thanks for the explanation.

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01 Aug 2009, 10:20
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let's say no. of revolution made by the larger rim = n/sec
28 *pi*x= 35*pi*n
therefore, n= (28*pi*x)/(35*pi)=4x/5
so in 1 min no of revolution = 60*(4x/5)=48x

so C

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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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22 Jan 2013, 06:29
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How to solve this question? IS this a rates problem?
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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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22 Jan 2013, 06:59
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fozzzy wrote:
How to solve this question? IS this a rates problem?

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches = $$\pi{d}=28\pi$$ inches. Hence, x revolutions per second = $$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.

Given that $$60*28\pi{x}=35\pi{n}$$ --> $$n=\frac{60*28\pi{x}}{35\pi}=48x$$.

Hope it's clear.
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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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03 Apr 2013, 13:13
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Ahem;

You don't need to involve pi - it's a constant that has no bearing on the solution.

The question is really just simple arithmetic - the sort of question that used to be posed to ten year olds.

If rim speeds are the same, and the small rim is rotating at x rps, then the large rim would be rotating at 28x/35 rps, or 60 x 28x/35 rpm = 48x rpm

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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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19 Jul 2013, 01:47
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Understanding the question:
Note that the question talks about 2 different metrics:
1) revolution per second which gives the number of revolution made in a second
2) inches per second - which is the distance travelled per second.
It is important to understand these 2 metrics and how they are related.

Facts to refer:
We know that: Distance travelled = Number of revolutions * Circumference of the circle
Extending that slightly to become rates: Distance travelled per second = Number of revolutions per second * Circumference of the circle.

What's given in the question:
Inches per second ie., distance per second is equal for 28 inch and 33 inch circles.
Number of revolutions per second by 28 inch = x

Number of revolutions per minute by 35 inch = ? Lets have this as variable a. Question asks this in terms of x, so there is no need to solve for x.

Solution:
Note that 28 inch is in seconds. Since we need the answer in minutes, lets convert that:
Number of revolutions per second by 28 inch = x*60
Applying the earlier stated formula: Distance travelled per second = Number of revolutions per second * Circumference of the circle, we have:
x*60*28*pi=a*35*pi
Solving this equation yields a= 48x.

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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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02 Aug 2013, 10:53
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

The larger rim must circulate for the same number of inches the smaller rim does.

C = (pi)d
C(small): (pi)*28
C(large): (pi)*35

Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches

(pi)*(1680) = (pi)*(35)(x)
pi*(48) = pi*(x)
48=x

I'm wondering if someone can help me with my equation here. I got it mostly correct, however, my final answer of x=48 wasn't quite the answer that is correct (48x) so I got a bit lucky in choosing it. I first multiplied the small rim by 60 seconds to get it in terms of one minute. I then set it equal to the circumference of the larger rim which I multiplied x to get the number of revolutions it would make so that distance covered by the two rims was the same. Can someone explain to me why this is not entirely correct?

Thanks!!

Here is my reasoning behind this question...I am not sure if it is correct or not but here it goes: The smaller rim rotates the same distance as the larger rim. This means that for a given time, the larger wheel rotates less. 28(pi) represents the smaller wheel and 28(pi)*(x) represents the number of revolutions it makes. 60*28*(pi)*x converts it into minutes (60 seconds/1 minute) as the question asks. On the other side of the equal sign is 35(pi). We are looking for the number of revolutions 35(pi) makes which we know to be a different number than the revolutions the smaller wheel makes, so we set it to n: 35(pi)*n. We are looking for the answer in terms of x so we should cancel out as much as possible while leaving x in the answer. Therefore, the final equation is 1680*(pi)*x = 35*(pi)*n ==> 48*(pi)*x = (pi)*n ==> 48x = n. Does that sound right?

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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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21 Aug 2013, 10:48
Bunuel wrote:
fozzzy wrote:
How to solve this question? IS this a rates problem?

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches = $$\pi{d}=28\pi$$ inches. Hence, x revolutions per second = $$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.

Given that $$60*28\pi{x}=35\pi{n}$$ --> $$n=\frac{60*28\pi{x}}{35\pi}=48x$$.

Hope it's clear.

1 revolution of a circle with the diameter of 28 inches = \pi{d}=28\pi inches. Hence, x revolutions per second = 28\pi{x} inches per second = 60*28\pi{x} inches per minute.

Couldn't understand why 60 has come into picture?
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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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21 Aug 2013, 10:52
honchos wrote:
Bunuel wrote:
fozzzy wrote:
How to solve this question? IS this a rates problem?

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches = $$\pi{d}=28\pi$$ inches. Hence, x revolutions per second = $$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.

Given that $$60*28\pi{x}=35\pi{n}$$ --> $$n=\frac{60*28\pi{x}}{35\pi}=48x$$.

Hope it's clear.

1 revolution of a circle with the diameter of 28 inches = \pi{d}=28\pi inches. Hence, x revolutions per second = 28\pi{x} inches per second = 60*28\pi{x} inches per minute.

Couldn't understand why 60 has come into picture?

$$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.
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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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21 Aug 2013, 10:55
28\pi{x} inches per second = 60*28\pi{x} inches per minute.

it should be actually divided by 60 to convert it into minutes?
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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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21 Aug 2013, 10:57
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honchos wrote:
28\pi{x} inches per second = 60*28\pi{x} inches per minute.

it should be actually divided by 60 to convert it into minutes?

10 inches per second. There are 60 seconds in minute so 60*10 inches per minute.
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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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21 Aug 2013, 11:16
Bunuel wrote:
honchos wrote:
28\pi{x} inches per second = 60*28\pi{x} inches per minute.

it should be actually divided by 60 to convert it into minutes?

10 inches per second. There are 60 seconds in minute so 60*10 inches per minute.

Correct I think i was tired thats the rason can't visualize that.

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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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10 Sep 2013, 18:18
WholeLottaLove wrote:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

The larger rim must circulate for the same number of inches the smaller rim does.

C = (pi)d
C(small): (pi)*28
C(large): (pi)*35

Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches

(pi)*(1680) = (pi)*(35)(x)
pi*(48) = pi*(x)
48=x

I'm wondering if someone can help me with my equation here. I got it mostly correct, however, my final answer of x=48 wasn't quite the answer that is correct (48x) so I got a bit lucky in choosing it. I first multiplied the small rim by 60 seconds to get it in terms of one minute. I then set it equal to the circumference of the larger rim which I multiplied x to get the number of revolutions it would make so that distance covered by the two rims was the same. Can someone explain to me why this is not entirely correct?

Thanks!!

Here is my reasoning behind this question...I am not sure if it is correct or not but here it goes: The smaller rim rotates the same distance as the larger rim. This means that for a given time, the larger wheel rotates less. 28(pi) represents the smaller wheel and 28(pi)*(x) represents the number of revolutions it makes. 60*28*(pi)*x converts it into minutes (60 seconds/1 minute) as the question asks. On the other side of the equal sign is 35(pi). We are looking for the number of revolutions 35(pi) makes which we know to be a different number than the revolutions the smaller wheel makes, so we set it to n: 35(pi)*n. We are looking for the answer in terms of x so we should cancel out as much as possible while leaving x in the answer. Therefore, the final equation is 1680*(pi)*x = 35*(pi)*n ==> 48*(pi)*x = (pi)*n ==> 48x = n. Does that sound right?

Hi,

Actually we should take as Distance travelled by smaller wheel per min = distance traveled by larger wheel per min
Distance traveled by smaller wheel per min = circumference * number of revolution per min
= pi*28*60 * x
Distance traveled by Larger wheel per min = circumference * Number of revolution per min
= pi*35*y
So
pi*28*60*x=pi*35*y
hence Number of revolution of larger wheel is =48x

Hope it helps

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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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11 Sep 2013, 21:57
Bunuel wrote:
fozzzy wrote:
How to solve this question? IS this a rates problem?

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches = $$\pi{d}=28\pi$$ inches. Hence, x revolutions per second = $$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.

Given that $$60*28\pi{x}=35\pi{n}$$ --> $$n=\frac{60*28\pi{x}}{35\pi}=48x$$.

Hope it's clear.

I'm still little unclear about how you equalise 60*28pi = 35pi*n
Is it because in the question it says that the inches covered by both the circles in a given time is same

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Re: A circular rim 28 inches in a diameter rotates the same [#permalink]

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12 Sep 2013, 02:50
b2bt wrote:
Bunuel wrote:
fozzzy wrote:
How to solve this question? IS this a rates problem?

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches = $$\pi{d}=28\pi$$ inches. Hence, x revolutions per second = $$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.

Given that $$60*28\pi{x}=35\pi{n}$$ --> $$n=\frac{60*28\pi{x}}{35\pi}=48x$$.

Hope it's clear.

I'm still little unclear about how you equalise 60*28pi = 35pi*n
Is it because in the question it says that the inches covered by both the circles in a given time is same

Yes.

The smaller rim = $$60*28\pi{x}$$ inches per minute.
The larger rim = $$35\pi{n}$$ inches per minute, where n is the number of revolution per minute.

We are told that those two are equal.

Does this make sense?
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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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13 Oct 2014, 00:14
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If x = 1, then the options would turn up as follows:

A. 48pi
B. 75
C. 48
D. 24
E. 1/75

Small circle circumference * 1 revolution $$= 2\pi * 14 * 1 = 28\pi$$

Large circle circumference * r revolution$$= 2\pi * 17.5 * r = 35\pi * r$$

Given that$$35\pi * r = 28\pi$$

$$r = \frac{4}{5} \frac{revolutions}{second} = \frac{4}{5} * 60 = 48 \frac{revolutions}{minute}$$

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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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19 Jan 2015, 01:02
One important thing to keep in mind right off the bat is that the smaller rim makes x revolutions per SECOND and they ask for how many revolutions per MINUTE the larger rim makes.

If the two rims rotate the same number of inches per second, then
28(pi)x/sec=35(pi)z/sec (with z being the number of rotations the larger rim makes per second)
so we want to isolate for z and we end up with
28(pi)x/35(pi)(sec)=z/sec
the pi's cancel out and we simplify it to
4/5x however we need to multiply it by 60, because the question asks for minutes, so the answer is 48x (C)
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Re: A circular rim 28 inches in diameter rotates the same number   [#permalink] 19 Jan 2015, 01:02

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