Answer: 13.5 minutes
Step-by-step explanation:
Given : Sophie can type 128 words in 3 minutes.
Then , rate of typing = [tex]\dfrac{\text{Number of words}}{\text{Time}}[/tex]
[tex]=\dfrac{128}{3}[/tex] (1)
Let x be the minute taken by her to type 576 words.
Then, rate of typing = [tex]\dfrac{576}{x}[/tex] (2)
From (1) and (2), we have
[tex]\dfrac{576}{x}=\dfrac{128}{3}\\\\\Rightarrow\ x=\dfrac{3\times576}{128}=13.5\text{ minutes}[/tex]
Hence, she will take 13.5 minutes to type 576 words.
