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A wheel has a diameter of x inches and a second wheel has a diameter

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A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 20 Jan 2015, 05:34
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A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 20 Jan 2015, 20:05
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[quote="Bunuel"]A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y


First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)

Now,
Revolutions = distance/circumference

So, from equation (1)
100 = d/(x*pi)
d = 100 * x * pi ---------- (3)

From equation (2)
Revolutions = d/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y

Answer (E)
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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 20 Jan 2015, 22:41
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d feet = 12d inches = 100 revolutions = 100*circumference = 100*(pi)*x
For same distance # revolutions for second wheel = distance/circumference = 100*pi*x/(pi*y) = 100x/y.

Answer E.


Bunuel wrote:
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.
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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 22 Jan 2015, 20:48
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Answer = E. 100x/y


............................ Wheel A ..................... Wheel B

Diameter .................. x .............................. y

Radius .................... \(\frac{x}{2}\) ............................ \(\frac{y}{2}\)

Circumference .......... \(\frac{d}{100}\) ......................... \(2\pi(\frac{y}{2})\) .............

\(2\pi(\frac{x}{2}) = \frac{d}{100}\)

\(d = 100\pi x\)

Revolutions of Wheel B to achieve distance d\(= \frac{100\pi x}{2\pi(\frac{y}{2})} = 100\frac{x}{y}\)
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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 15 Feb 2016, 08:57
Bunuel wrote:
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.


A very simple Question

Circumference of a circle = pi * D = distance covered in one revolution.
For first circle, one revolution = pi*x
In 100 revolutions, distance covered = 100* pi*x = d feet
Second wheel in one revolution = pi*y
For d feet or for 100*pi*x it will take 100*pi*x / pi*y

or, 100x/y
Answer E

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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 14 May 2016, 07:00
Bunuel wrote:
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y


Quote:
A wheel has a diameter of x inches..... covers a distance of d feet in 100 revolutions.


So, \(d\) = \(100*2π*\frac{x}{4}\)

Quote:
A second wheel has a diameter of y inches....How many revolutions does the second wheel make in covering d feet..


Circumference of the second wheel is \(2π*\frac{y}{4}\)

Quote:
How many revolutions does the second wheel make


=> \((100*2π*x/4) / (2π*y/4)\)

=> \(\frac{100x}{y}\)

Hence answer will be (E) \(\frac{100x}{y}\)
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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 14 May 2016, 23:34
A wheel covers 2πr distance in one revolution. where r= diameter/2

First wheel covers d feet in 100 rev. => d= 100* 2π * (x/2)

Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)

comparing both equations:-

=> p= (100∗2π∗x/2)/(2π∗y/2)

=> 100x/y

OA :- E
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Re: A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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New post 12 Mar 2018, 15:26
Bunuel wrote:
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y


Recall that d feet = 12d inches and the circumference (C = 2πr or Dπ) of the x-inch diameter wheel = xπ and that of the y-inch diameter wheel = yπ.

Therefore, we know that in 1 revolution, the first wheel covers a distance of xπ inches. Thus, in 100 revolutions, it covers 12d inches, as shown here:
xπ * 100 = 12d

If we let r = the number of revolutions the second wheel makes, we have:

yπ * r = 12d

Thus, we have:

xπ * 100 = yπ * r

100x = yr

100x/y = r

Answer: E
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Re: A wheel has a diameter of x inches and a second wheel has a diameter &nbs [#permalink] 12 Mar 2018, 15:26
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