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?
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Number of revolutions
Source: Beat The GMAT — Problem Solving |
Rear Wheels :
Radius : r
Front Wheels :
Radius : r/2
Circumfrence of Front wheels = 1m
Hence, 2*PI*r = 1m
==> 2*pi*r/2 = 1m
==> r=1/pi
Now Circumfrence of Rear wheel : 2*pi*r = 2*pi*1/pi
=2m
Now in 1 revolution(circumfrence) the rear wheel covers 2m
Therefore to cover,1000m(1km),No of rev = 1000/2=500.
Its got to be 500!
Radius : r
Front Wheels :
Radius : r/2
Circumfrence of Front wheels = 1m
Hence, 2*PI*r = 1m
==> 2*pi*r/2 = 1m
==> r=1/pi
Now Circumfrence of Rear wheel : 2*pi*r = 2*pi*1/pi
=2m
Now in 1 revolution(circumfrence) the rear wheel covers 2m
Therefore to cover,1000m(1km),No of rev = 1000/2=500.
Its got to be 500!
i think its 250/pi.
Assume that the front wheel has a radius X, ==> rear wheel has a radius 2X.
the circumference of the front wheel is 2*pi*x==> 2pi
The number of revolutions of the front wheel per one kilometer is 1000/2pi=500/pi.
Since the circumference of the rear wheel is twice the length of the front (hence 2*pi*2x=4pi) hence the number of revolutions for the rear wheel must be (500/pi)/2=250/pi
Assume that the front wheel has a radius X, ==> rear wheel has a radius 2X.
the circumference of the front wheel is 2*pi*x==> 2pi
The number of revolutions of the front wheel per one kilometer is 1000/2pi=500/pi.
Since the circumference of the rear wheel is twice the length of the front (hence 2*pi*2x=4pi) hence the number of revolutions for the rear wheel must be (500/pi)/2=250/pi
