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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
Posts: 44298
A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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14 May 2016, 04:00
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Question Stats:

89% (01:06) correct 11% (01:00) wrong based on 62 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
[Reveal] Spoiler: OA

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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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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   [#permalink] 12 Mar 2018, 16:26
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