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Manager  Joined: 23 Mar 2008
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A circular rim 28 inches in diameter rotates the same number  [#permalink]

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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. $$\frac{48\pi}{x}$$

B. $$75x$$

C. $$48x$$

D. $$24x$$

E. $$\frac{x}{75}$$

PS88602.01

Originally posted by puma on 08 Jun 2008, 11:01.
Last edited by Bunuel on 21 Sep 2019, 06:29, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert V
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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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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2
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.
##### General Discussion
Director  Joined: 23 Sep 2007
Posts: 571
Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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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
Manager  Joined: 10 Mar 2008
Posts: 50
Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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3
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
Manager  Joined: 21 Jun 2009
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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thanks for the explanation.
Intern  Joined: 22 Mar 2008
Posts: 35
Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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2
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 diameter rotates the same number  [#permalink]

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1
How to solve this question? IS this a rates problem?
Intern  Joined: 03 Apr 2013
Posts: 1
Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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1
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
Senior Manager  Joined: 13 May 2013
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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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 ?

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 diameter rotates the same number  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 64216
Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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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 diameter rotates the same number  [#permalink]

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

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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 diameter rotates the same number  [#permalink]

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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.

You are amazing man.!
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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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 diameter rotates the same number  [#permalink]

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

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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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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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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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