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The circumference of the front wheel of a cart is 30 ft long

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The circumference of the front wheel of a cart is 30 ft long [#permalink]

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New post 19 Feb 2010, 13:43
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The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?

A. 20 ft
B. 25 ft
C. 750 ft
D. 900 ft
E. 1000 ft
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Oct 2012, 06:09, edited 1 time in total.
Edited the question and added the OA.

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Re: The circumference of the front wheel [#permalink]

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New post 19 Feb 2010, 13:54
AtifS wrote:
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?
A. 20 ft
B. 25 ft
C. 750 ft
D. 900 ft
E. 1000 ft

Any thoughts guys?

@Moderators, please! MERGE IT IF ALREADY POSTED.


Answer is D. 900/36 ~ 25 (backwheel revolution) = 900/30 ~ 30 front wheel revolution

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Re: The circumference of the front wheel [#permalink]

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New post 19 Feb 2010, 13:56
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- for one full revolutions of rear wheel, front wheel would revolve 1 + 1/5 revolutions(36(rear wheel) = 30(front wheel) + 30/5(additional distance travelled by front wheel after it completed ONE FULL revolution))
- so event 5 revolutions of rear wheel will have 6 revolutions of front wheel.
- so 25 revolutions of rear wheel will have 30 revolutions of front wheel(5 more than the rear wheel as asked)

= 25 * 36 = 900

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Re: The circumference of the front wheel [#permalink]

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New post 19 Feb 2010, 14:11
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Plug in the options.
A and B are ruled out because they are less for 5 revolutions.
Go to C, is 750/30 - 750/36 = 5 ? No.
Go to D, is 900/30 - 900/36 = 5 ? Yes!

D it is.
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Re: The circumference of the front wheel [#permalink]

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New post 20 Feb 2010, 00:14
Guys! thank you for your valuable explanation. I t really made easy to understand the question.

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Re: The circumference of the front wheel [#permalink]

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New post 16 Oct 2012, 01:22
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C1=30 ft, C2=36 ft
If Rotation1=x, d(distance)=Cx
30(x+5)=36x, x=25, d=30(25+5)=30x30=900

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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New post 18 Jul 2013, 22:43
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Point to note: Both the wheels would have travelled the same distance.
Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).
Equating the distance travelled by front wheel to back wheel: (x+5)*30 = x * 36. (Formula for calculating the distance travelled by each wheel is: # of revolutions * circumference.)
Solving this eqn. gives x=25.
Sub x=25 either in (x+5)*30 or in x * 36 to get the distance, which is 900. So the correct choice is D.

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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AtifS wrote:
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?

A. 20 ft
B. 25 ft
C. 750 ft
D. 900 ft
E. 1000 ft


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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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New post 22 Jul 2013, 02:55
Bunuel wrote:


Both the questions need a different perspective of thinking. Thanks Bunuel for providing links to these questions!

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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AtifS wrote:
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?

A. 20 ft
B. 25 ft
C. 750 ft
D. 900 ft
E. 1000 ft


Good one.

X/30 - X/36 = 5

X= 900

Cheers
J :)

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]

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New post 12 Jan 2017, 20:38
Treat what they give us in the problem as a rate:

A: 1 rev/30 ft
B: 1 rev/36 ft
D = distance

D(A) = 5+D(B)
D(1/30) = 5+(1/36)
D(36-30) = 5400
6D = 5400 --> D = 900 ft

D.

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Re: The circumference of the front wheel of a cart is 30 ft long   [#permalink] 12 Jan 2017, 20:38
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