Sorry for the late reply, but building on the above concept this might shed some more light
diameter = 8 cms
circumference = 1 rev = pi*8
1000 revs --> 1 min
1000 "Circumferences" --> 1 min
1000 * pi*d --> 1 min
1000 * pi*8 --> 1 min
8000pi --> 1 min
(i.e the wheel travels a distance of 8000pi cms in a minute.. they can ask how much in x minutes etc on the gmat)
Dekho, the crux is --> 1 circumference = a single revolution (360 degrees)
Found this one via google:
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
Bigger wheel --> 1 rev = 1 circumference = 36 ft
Smaller wheel --> 1 rev = 1 circumference = 30 ft
Imagine that the cart is moving towards the left.
Now, the gap between the two wheels would
always be constant and thus the distance travelled by the two wheels would also be constant.
To travel the same distance its obvious that the smaller would require more revs than the bigger one. This is stated in the question too (5 more revs than the bigger one)
Let the revs of the bigger one be x (ie the number of revolutions required to travel a certain distance), then the smaller one would require x+5 revs to travel the same distance.
Bigger wheel -->
1 rev = 36 ft
x revs = 36 * x ft
Smaller wheel -->
1 rev = 30 ft
x +5 revs = 30 * (x + 5) ft
Ultimately the distance should be the same, so we can equate them:
36 * x = 30 * (x + 5)
6 * x = 150
x = 25 ( No of revolutions)
To find the distance travelled by the cart just plug in x = 25 in the equation of any one of the wheel.
36 * 25 = 900
[spoiler]OA: D. 900 ft[/spoiler]
Regards,
Vivek
