One wheel has a diameter of 30 inches and a second wheel has a diameter of 20 inches. The first wheel traveled a certain distance in 240 revolutions. In how many revolutions did the second wheel travel the same distance?

not just an answer please

A.120
B.160
C.360
D.420
E.480

short way:

the number of revolutions varies inversely with the diameter of the wheel
i.e. the larger the wheel the smaller the number of revs.

R1/R2 = C2/C1
240/R2 = 20/30
20R2 = 7200
R2 = 360

or

distance covered by first wheel = 2π(15)(240) = 7200π inches

circumference of 2nd wheel = 2π(10) = 20π inches
for the same distance of 7200π inches
number of revolutions = 7200π/(20π) = 360 revs

c.360

Well, well, well, it seems we have a wheel-y interesting problem here! So we have two wheels, one with a diameter of 30 inches and the other with a diameter of 20 inches. The first wheel went on quite the adventure, traveling a certain distance in 240 revolutions. Now we want to know how many revolutions the second wheel traveled to cover the same distance.

Now, let's roll with some math. Remember, the circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. So, the circumference of the first wheel is π times 30 inches, and the circumference of the second wheel is π times 20 inches.

Since we know that the first wheel traveled the same distance in 240 revolutions, we can simply multiply the circumference of the first wheel by 240 to find the total distance it traveled. Now we need to figure out how many revolutions the second wheel needs to cover that same distance.

Here's the catch - the distance is the same, but the circumferences are different! So, in order for the second wheel to cover the same distance, it needs to rotate more times because its circumference is smaller.

The ratio between the two circumferences is 30/20, which simplifies to 3/2. That means for every 2 revolutions of the first wheel, the second wheel will need to make 3 revolutions to cover the same distance.

So, if the first wheel made 240 revolutions, we can set up a proportion: 2/240 = 3/x, where x represents the number of revolutions the second wheel would make.

Cross multiply that bad boy, and we get 2x = 3 * 240. Solving for x, we find that the second wheel made 3 * 240 / 2 = 360 revolutions to cover the same distance as the first wheel.

So my witty answer is C.360! The second wheel had to work its way around 360 times to keep up with the first wheel's crazy adventure!

To solve this problem, we can use the concept that the circumference of a circle is directly proportional to its diameter.

The circumference of the first wheel can be calculated using the formula:
C1 = π * d1
Where C1 is the circumference of the first wheel and d1 is its diameter.

Similarly, the circumference of the second wheel can be calculated using the formula:
C2 = π * d2
Where C2 is the circumference of the second wheel and d2 is its diameter.

We are given that the first wheel traveled a certain distance in 240 revolutions. Let's denote the distance traveled by D.

The distance traveled by the first wheel in terms of its circumference can be calculated using the formula:
D = C1 * number of revolutions

Similarly, the distance traveled by the second wheel can be calculated using the formula:
D = C2 * number of revolutions

Since the distance traveled is the same for both wheels, we can set the two equations equal to each other:
C1 * number of revolutions (first wheel) = C2 * number of revolutions (second wheel)

We can substitute the formulas for C1 and C2:
(π * d1) * number of revolutions (first wheel) = (π * d2) * number of revolutions (second wheel)

π and the number of revolutions cancel out on both sides, so we are left with:
d1 = d2 * number of revolutions (second wheel)

We can solve for the number of revolutions (second wheel):
number of revolutions (second wheel) = d1 / d2

Substituting the given values:
number of revolutions (second wheel) = 30 inches / 20 inches
number of revolutions (second wheel) = 1.5

Since we can't have fractional revolutions, we round the value to the nearest whole number.

Therefore, the second wheel traveled in 2 revolutions (approximately).

The correct answer is not listed among the options provided.

To solve this problem, we need to compare the distances traveled by both wheels.

First, let's determine the circumference of each wheel, which is the distance traveled in one revolution. The formula to calculate the circumference is C = π * d, where C is the circumference, π is a mathematical constant (approximately equal to 3.14), and d is the diameter of the wheel.

For the first wheel with a diameter of 30 inches, the circumference is C1 = π * 30 inches.

For the second wheel with a diameter of 20 inches, the circumference is C2 = π * 20 inches.

Now, we know that the first wheel traveled a certain distance in 240 revolutions. So, the total distance covered by the first wheel is D1 = 240 * C1.

To find out how many revolutions the second wheel needs to travel the same distance, we need to divide the total distance covered by the first wheel by the circumference of the second wheel.

Total revolutions of second wheel = D1 / C2 = (240 * C1) / C2.

Substituting in the values we already found, the total revolutions of the second wheel = (240 * π * 30 inches) / (π * 20 inches).

Simplifying this further, the π cancels out, and we get total revolutions of the second wheel = (240 * 30 inches) / 20 inches.

Calculating this, the total revolutions of the second wheel = 360 revolutions.

Therefore, the second wheel traveled the same distance in 360 revolutions, which corresponds to option C.