There are two wheels with diameter 30 inches and 20 inches. The first wheel covers a certain distance in 240 revolutions. In how many revoluions would the second wheel cover the same distance?
dwould it be proportional? The linear distances their circumferences are in a set proportion.
30/240=20/N
bobpursley,
Thanks for your responce and help, I don't think so it's proportional. Since the answer is 360 revolutions.
And putting them in proportions doesn't give the correct answer.
A friend told me this solution;
Find the circumference of both the wheels by formula 2 pi r:
1st wheel: 94.2 inches.
2nd wheel: 62.8 inches.
Now multiply the circumference of the 1st wheel by revolutions:
94.2*240 = 22608 inches.
This would be the otal distance traveled by wheels.
Now divide the distance by the circumference of second wheel,
you'll get no. of revolutions:
No. of revolutions: 22608/62.8
No. of revolutions: 360 revolutions.
To determine the number of revolutions the second wheel would cover to travel the same distance as the first wheel, we can set up a proportion using the ratio of their diameters.
The distance covered by a wheel in one revolution is equal to the circumference of the wheel, which can be calculated using the formula: circumference = π * diameter.
Let's first find the circumference of each wheel:
For the first wheel with a diameter of 30 inches:
Circumference of the first wheel = π * 30 = 30π inches
For the second wheel with a diameter of 20 inches:
Circumference of the second wheel = π * 20 = 20π inches
Now, we can set up a proportion:
(distance covered by first wheel) / (number of revolutions of first wheel) = (distance covered by second wheel) / (number of revolutions of second wheel)
Since the distance covered is the same for both wheels, we can substitute the values:
(30π inches) / (240 revolutions of the first wheel) = (20π inches) / x (number of revolutions of the second wheel)
Cross multiplying, we get:
30π * x = 20π * 240
Simplifying, we have:
30x = 20 * 240
Dividing both sides by 20, we get:
x = (20 * 240) / 30
x = 160
Therefore, the second wheel would cover the same distance in 160 revolutions.