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

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AtifS
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The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   Updated on: 16 Oct 2012, 06:09
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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
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D

Originally posted by AtifS on 19 Feb 2010, 13:43.
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] 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 [#permalink] 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

D
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Re: The circumference of the front wheel [#permalink] New post   19 Feb 2010, 13:54
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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

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] 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] 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 of a cart is 30 ft long [#permalink] 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] New post   18 Jul 2013, 22:46
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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


Similar questions to practice:
two-wheels-are-connected-via-a-conveyor-belt-the-larger-133697.html
how-long-in-minutes-did-it-take-a-bicycle-wheel-to-roll-130026.html
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   22 Jul 2013, 02:55
Bunuel wrote:
Similar questions to practice:
two-wheels-are-connected-via-a-conveyor-belt-the-larger-133697.html
how-long-in-minutes-did-it-take-a-bicycle-wheel-to-roll-130026.html


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] New post   21 Nov 2013, 14:42
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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] 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] New post   14 Jun 2018, 05:43
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Let the no. of rotations of the back wheel be x. Thus the rotations of the front wheel = x + 5

the distance traveled by the wheels will be the same. (No. of rotations * circumference)

Distance traveled by front wheel (D1) = 30 * (x+5)
Distance traveled by front wheel (D2) = 36 * x

therefore, 36x = 30(x+5)
36x = 30x + 150
6x = 150
x = 150/6 = 25

To calculate the distance traveled, substitute the above value in either D1 or D2.

D1 = 30 * ( 25 + 5 ) = 900.

Correct Answer : D
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   14 Jun 2018, 13:26
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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



For every one revolution of front wheel, the back wheel revolves (30/36) = 5/6th of revolution.

hence for every 6 revolutions of front wheel, the back wheel performs 5 revolutions. hence front wheel has performed 1 more revolution than back wheel.

Therefore for front wheel to perform 5 more revolutions than back wheel, it needs to perform 30 revolutions & back wheel will perform 25 revolutions.

In 30 revolutions of the front wheel the cart has moved by (30*30) = 900 ft

Alternate Solution:

The distance traveled will be a multiple of LCM of (30,36), only answer choice D, is possible.


Answer D.


Thanks,
GyM
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   14 Jun 2018, 13:42
Plug and play works well here. Also, it's usually helpful to pick a choice that has a smart number. I like 900 because it is divisible by both 30 and 36; thus, 900 / 30 - 900 / 36 should equal 5. It does; hence, D is the answer.
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   17 Jun 2018, 19:33
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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


Since the total distance traveled by the front wheel must be equal to that of the back wheel, the number of times the front wheel revolves must be 5 more than the number of times the back wheel revolves. Thus, if we let x = the number of times the back wheel revolves, we have:

36x = 30(x + 5)

36x = 30x + 150

6x = 150

x = 25

In 25 revolutions, the back wheel traveled 36 x 25 = 900 ft.

Answer: D
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   16 Feb 2020, 23:14
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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


The video solution explains the CONCEPT of WHEELS and explains the problems as well

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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   12 Mar 2023, 01:27
1) the front wheel traveled 150 more.
2) the difference between front and back wheels is 6.
3) 150/6 = 25. this means that the back wheel had to travel 25 revolutions. 25x36 = 900.

good reasoning ?
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink] New post   14 Mar 2024, 23:53
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Re: The circumference of the front wheel of a cart is 30 ft long [#permalink]
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