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Wheel Revolutions

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by harsh.champ » Fri Feb 19, 2010 8:02 am
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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by sadullaevd » Fri Feb 19, 2010 8:11 am
Diameters: X and Y

One Rotation distance: X pi and Y pi

Then --> d=100Xpi and d = R(variable for Rotation) Ypi

Putting them together: RYpi=100Xpi

R=100x/y

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by thephoenix » Fri Feb 19, 2010 8:18 am
harsh.champ 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
one rev of x inch dia wheel=pix inch
100 rev=100 pi *x inch=12d inch

one rev of y inch dia wheel=pi * y inch

or pi*y inch = 1 rev of y inch dia wheel
so 12d inch =[1/(pi*y)] *12d=put 12d from eqn 1=100 *pi *x/pi*y=100 x/y =E
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by kstv » Fri Feb 19, 2010 8:22 am
IMO E
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by shashank.ism » Fri Feb 19, 2010 10:32 pm
harsh.champ 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
so for 1st wheel 2pi x = d/100 --> d= 100 (2pi x )
for 2nd wheel 2pi y = d/rev --> rev = d/(2 pi y) --> rev = 100 (2pi x )/2 pi y = [spoiler]100x/y Ans E[/spoiler]
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by Jeff@TargetTestPrep » Mon Mar 12, 2018 3:37 pm
harsh.champ 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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