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

Question

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.

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

co801dw · Accepted Answer

C1=30 ft, C2=36 ft
If Rotation1=x, d(distance)=Cx
30(x+5)=36x, x=25, d=30(25+5)=30x30=900

jlgdr · Answer

Good one. X/30 - X/36 = 5 X= 900 Cheers J

ISBtarget · Answer

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

chix475ntu · Answer

- 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

vscid · Answer

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.

AtifS · Answer

Guys! thank you for your valuable explanation. I t really made easy to understand the question.

Kudos

Jaisri · Answer

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.

Bunuel · Answer

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

Jaisri · Answer

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

law258 · Answer

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.

ColonelRed · Answer

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

GyMrAT · Answer

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

ColumbiaEMBA · Answer

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.

JeffTargetTestPrep · Answer

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

GMATinsight · Answer

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

https://www.youtube.com/watch?v=IX99uoqf78Y

joe123x · Answer

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 ?

Natansha · Answer

Hi  KarishmaB  I had a very small doubt in this, how can we equate the distance travelled by front & back wheel, as front wheels would always travel a little extra than the back ones depending on the distance between the front & back wheels.

Bunuel · Answer

Imagine the back wheel touches the ground at point 0 and the front wheel at point 10. If the vehicle moves 20 meters forward, the back wheel is now at 20 and the front wheel at 30. Each wheel has shifted 20 meters from its original position, so both wheels travel the same distance.

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

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