Question

A giant hummingbird flaps its wings į times as fast as a bee hummingbird. If a giant hummingbird flaps its wings 10 times per second, write and solve an equation to show how many times a bee hummingbird flaps its wings per second.

a) ( 20/3 ) times per second
b) ( 3/20 ) times per second
c) ( 1/3 ) times per second
d) ( 30 ) times per second

Answer 1

b)
`\( (3)/(20) \)` times per second

Step-by-step explanation:

To express the relationship between the wing-flapping rates of the giant hummingbird
`(\(G\))` and the bee hummingbird
`(\(B\))`, we use the given information that the giant hummingbird flaps its wings
`\( (i)/(3) \)` times as fast as a bee hummingbird. Let
`\( f_G \)` and
`\( f_B \)` represent the wing-flapping rates of the giant and bee hummingbirds, respectively. The equation representing this relationship is
`\( f_G = (1)/(3) f_B \)`. Given that the giant hummingbird flaps its wings 10 times per second
`(\( f_G = 10 \)` times per second), we can substitute this value into the equation and solve for
`\( f_B \):`

`\[ 10 = (1)/(3) f_B \]`

Multiplying both sides by 3 to isolate
`\( f_B \)`:

`\[ f_B = 3 * 10 = 30 \]`

So, the bee hummingbird flaps its wings 30 times per second. However, the question asks for the answer in the form of a fraction. To express 30 as a fraction, we can write it as
`\( (30)/(1) \)`. Since
`\( f_B \)` represents the wing-flapping rate of the bee hummingbird, the final answer is
`\( (1)/(f_B) = (1)/(30) \)` times per second. Therefore, option b)
`\( (3)/(20) \)` times per second is the correct answer. Understanding the given ratio and applying it to solve for the specific quantity asked helps in interpreting and solving such proportional relationships in mathematics.