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

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Math Expert
Joined: 02 Sep 2009
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A wheel has a diameter of x inches and a second wheel has a diameter  [#permalink]

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20 Jan 2015, 06:34
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15% (low)

Question Stats:

82% (01:01) correct 18% (00:47) wrong based on 92 sessions

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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

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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20 Jan 2015, 21:05
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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

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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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20 Jan 2015, 23:41
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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.

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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22 Jan 2015, 21:48
1

............................ 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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15 Feb 2016, 09:57
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

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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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14 May 2016, 08:00
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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15 May 2016, 00:34
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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14 Oct 2017, 07:47
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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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12 Mar 2018, 16:26
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

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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, 16:26
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