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

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Intern
Joined: 23 Mar 2015
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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26 Mar 2015, 08:23
Hey guys, A simple application of kinematics.

V1= linear velocity of the rim of small diameter.

V2= linear velocity of the rim of large diameter.

r1 =radius of smaller rim, i.e. (28/2= 14 in)

r2= radius of larger rim, i.e. (35/2 =17.5 in)

w1=2*pi*f1= angular velocity(w1) and frequency(f1) of rotation of smaller rim.

W2=2*pi*f2= angular velocity(w2) and frequency(f2) of larger rim.

Acc. to the query v1=v2 which implies,

or, 2*pi*r1*f1 = 2*pi*r2*f2

or, 2*22/7*14*f1 = 2*22/7*17.5*f2

or, 88f1=110f2

or, f2= (4/5)f1

but, revolution per MINUTE is being asked, then

or, f2=(4/5)*60*f1

therefore, f2 = 48f1.

Thus option C is opted thus.

Posted from my mobile device
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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14 Oct 2015, 18:56
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 am little bit confused about the wording, it says rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter, so a how a 28 inch diameter rim rotate same number of inch per second as a 35 inch ?? suppose 28 diameter rotates 10 then 35 diameter rotates 10 so their circumeference must be different but how their circumference will be equal??
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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02 May 2016, 08:30
puma 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 ?

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

Here is an alternate time saving solution with the use of ratios.
Now the ratio of the rims circumferences will be same as the ratio of their radii.(find out why ) Now R/r=35/28=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 larger circle will have a lower revolution speed than smaller.
Now a,e,b are out. Left only c and d.
Now we know revolution = x per sec. So 60x/min. So larger rim rev=60x*(inversed ratio)= 60x*4/5= 48x
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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22 Jul 2016, 22:28
puma 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 ?

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

One rotation of the wheel is equal to its circumference = pi*diameter

Total distance covered in t time will be = pi*d*rate of revolution *time taken

Now the distance covered is equal for both the wheels, in 1second therefore -
28pi*x*1sec=35pi*R*1sec
28x=35R
R=28x/35
This is the rate for bigger 35 inch wheel per second
In one minute the bigger will cover Rate *time (60 seconds) = (28x/35) *60 ---> 48x

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

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26 May 2017, 10:32
puma 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 ?

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

Okay..here it goes..

Lets call the smaller one A and the larger one B.

A's diameter = $$28$$, so circumference = $$28\pi$$
B's diameter = $$35$$, so circumference = $$35\pi$$

Let the number of revolutions of A = x, and those of B = y.
According to the question..
$$28\pi*x = 35\pi*y$$

Thus,

$$y = \frac{4}{5}x$$

But that's the value of revolutions per second. For per minute..multiply it with 60.

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

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28 May 2017, 23:51
puma 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 ?

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

1. We will convert x revolutions per second of the smaller rim as 60x revolutions per minute
2. The distance rotated per second is the same for both but since the diameters are different, we know that the larger rim makes lesser revolutions per second
3. The ratio of the number of revolutions of the two rims are given by the inverse of the ratio of their diameters.
4. So the number of revolutions per minute of the larger rim is 60x *(28/35) = 48x.
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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30 Jan 2018, 10:27
puma 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 ?

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

The smaller rim rotates at a rate of 28πx inches per second. Since the larger rim rotates the same number of inches per second, it rotates at a rate of 28πx inches per second also, and, in one minute, it rotates 28πx * 60 inches.

Since 1 rotation of the larger rim = its circumference = 35π, the number of rotations made by the larger rim will thus be:

(28πx * 60)/35π

(4x * 60)/ 5

4x * 12

48x

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

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17 Aug 2018, 15:56
puma 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 ?

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

We can even not to write formulas for circumference and so on.

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter - this says us that a bigger rim makes a revolution slightly less frequently (slower) than a smaller rim.

the smaller rim makes x revolutions per second ---> it makes 60x revolutions per minute.

So, the bigger rim will make a little smaller amount of revolutions per minute ---> only C fits.
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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28 Feb 2019, 12:13
1) Make a chart and plug in easy value of 7 for rate:

____distance____rate______time
Small = 28 _____ 7 in _____ 4 sec --->x = 7/4 inches per sec
Big = 35 _______ 7 in _____ 5 sec

2) If Big rotates 7 inches in 5 sec ---> *12 = 84 inch total rotation per 1 min

3) Test our values against answers, starting with C
48*(7/4) = 84
12*7= 84
This matches, so it's the correct answer.
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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22 Sep 2019, 15:53
If in 1 second the larger rim does the same inches as the smaller one then in 1 second the larger rim does (x)*28*pi inches. In one minute the larger rim will do 60 *(x)*pi*28 inches. For the larger rim, to to see how many complete revolutions that is for it,we must divide 60 *(x)*pi*28 inches by 35pi. This gives us 48x. ANSWER IS C
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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22 Sep 2019, 15:57
If in 1 second the larger rim does the same inches as the smaller one then in 1 second the larger rim does (x)*28*pi inches. In one minute the larger rim will do 60 *(x)*pi*28 inches. For the larger rim, to to see how many complete revolutions that is for it,we must divide 60 *(x)*pi*28 inches by 35pi. This gives us 48x. ANSWER IS C
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A circular rim 28 inches in diameter rotates the same number  [#permalink]

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28 May 2020, 10:26
Concept to first understand: With 1 revolution, a rim will travel the distance equal to that of its circumference. (Think about it)

Small Rim
Diameter = 28
Circumference = 28Pi
In 1 second, it makes x revolutions, so distance traveled = 28Pi(x)...........(1)

Large rim
Diameter = 35
Circumference = 35Pi
Assume in 1 second, it makes 'n' revolutions, so distance traveled = 35Pi(n)..........(2)

Now, the question says that the larger rim travels the same distance as the smaller rim per second (i.e; rotates the same number of inches). Thus, when you equate equations (1) and (2) - you get Number of revolutions by large rim (n) in terms of number of revolutions by the small rim (x) in 1 second.

35Pi(n) = 28Pi(x)
n = 4x/5 (per second)

Therefore in a minute, the larger rim makes 60n revolutions = (4x/5) * 60 = 48x

Hence the answer is C: 48x
A circular rim 28 inches in diameter rotates the same number   [#permalink] 28 May 2020, 10:26

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