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The radius of the front wheels of a cart is half the radius of its rea

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Bunuel
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The radius of the front wheels of a cart is half the radius of its rea [#permalink] New post   08 Sep 2020, 01:00
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The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?

A. \(\frac{250}{\pi}\)
B. \(\frac{500}{\pi}\)
C. 250
D. 500
E. 750


M10-28

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D
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yashikaaggarwal
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Re: The radius of the front wheels of a cart is half the radius of its rea [#permalink] New post   08 Sep 2020, 01:25
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Let the radius of front wheel of cart be r
The circumference is = 1 meter
Circumference = 2πr
1 = 2πr

Radius of rear wheel = 2r
Circumference will be 2*π*2r
=> 2*(2πr)
=> 2(1)
=> 2 metre.

The front wheel revolved 1000m/1 = 1000 times (1km = 1000m)

The rear wheel revolved 1000m/2 = 500 times

Answer is D

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Re: The radius of the front wheels of a cart is half the radius of its rea [#permalink] New post   08 Sep 2020, 02:07
The radius of the front wheels of a cart is half that of the rear wheels. If the circumference of the front wheels is 1 meter and the cart traveled 1 kilometer, how many revolutions did the rear wheels make?

\(R_f= \frac{1}{2} * R_r\)

\(2 π R_f= 1 meter\); \( R_f= \frac{1}{2π} meter\)

\(R_r= \frac{1}{π} meter\)

1 revolutions did the rear wheels make= 2 π \(R_r\)= 2 meter = \(\frac{2}{1000}\) km

In 1 km it will make = \(\frac{1000}{2}\) revolution= 500 Rev


A.\(\frac{ 250}{π}\)

B.\( \frac{500}{π}\)

C. 250

D. 500

E. 750
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Bunuel
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Re: The radius of the front wheels of a cart is half the radius of its rea [#permalink] New post   01 May 2023, 12:32
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Bunuel wrote:
The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?

A. \(\frac{250}{\pi}\)
B. \(\frac{500}{\pi}\)
C. 250
D. 500
E. 750


M10-28


Official Solution:

The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?

A. \(\frac{250}{\pi}\)
B. \(\frac{500}{\pi}\)
C. 250
D. 500
E. 750


Since the radius of the rear wheels is twice the radius of the front wheels, the circumference of the rear wheels is also twice that of the front wheels, making it 2 meters. To calculate the number of revolutions made by each rear wheel when traveling 1,000 meters, divide the total distance by the circumference: (1,000 meters)/(2 meters) = 500 revolutions.


Answer: D
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Re: The radius of the front wheels of a cart is half the radius of its rea [#permalink]
01 May 2023, 12:32
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