This is an SAT prep question. Senai customized her bicycle by exchanging the front wheel for a wheel that had one half the diameter of the back wheel. Now Senai rides the bicycle, how many revolution does the front wheel make for each revolution on the back wheel?
A)8
B)4
C)2
D)1/2
E)1/4
Diameter big wheel = D
diameter little wheel = D/2
In one revolution, the back wheel goes forward pi D
meanwhile the forward wheel also has to go forward pi D, which is 2 pi (D/2)
so the little wheel makes two revolutions for each of thew big wheel
i don't knw
To determine how many revolutions the front wheel makes for each revolution on the back wheel, we need to compare their circumferences.
The circumference of a wheel is given by the formula C = 2πr, where C is the circumference and r is the radius.
Let's assume that the radius of the back wheel is r. So, the circumference of the back wheel is C_back = 2πr.
According to the question, the front wheel has half the diameter of the back wheel. Since diameter is twice the radius, the radius of the front wheel is r/2. So, the circumference of the front wheel is C_front = 2π(r/2) = πr.
To find the ratio of the front wheel's circumference to the back wheel's circumference, we can divide C_front by C_back:
C_front / C_back = (πr) / (2πr) = 1/2
Therefore, for each revolution of the back wheel, the front wheel makes 1/2 revolution.
Hence, the answer is D) 1/2.
To solve this SAT prep question, we need to first understand the relationship between the front and back wheels after Senai made the customization. The important information here is that the front wheel has one half the diameter of the back wheel.
Now, let's think about the relationship between the radius of a wheel and the number of revolutions it makes. The distance traveled by a wheel in one revolution is equal to its circumference. And the circumference of a wheel is calculated by multiplying the diameter by pi (π).
In this case, since the front wheel has half the diameter of the back wheel, it means that the front wheel's circumference is also half the circumference of the back wheel.
Now, let's analyze the multiple-choice options:
A) 8
B) 4
C) 2
D) 1/2
E) 1/4
If the front wheel makes 8 revolutions for each revolution of the back wheel, then its circumference would be 8 times the circumference of the back wheel. However, since the front wheel has half the circumference, this option is not correct.
If the front wheel makes 4 revolutions, the same reasoning applies. It would mean that its circumference is four times the circumference of the back wheel, which is not the case.
If the front wheel makes 2 revolutions, then its circumference is two times the circumference of the back wheel. However, this is not what we know from the question. The front wheel's circumference is half the circumference of the back wheel.
If the front wheel makes 1/2 revolution, then its circumference would be half the circumference of the back wheel. This matches the information provided in the question, so option D) is the correct answer.
Therefore, the correct answer to this SAT prep question is D) 1/2.