tanvi finds that her robot vacuum can clean her 150 - square - foot kitchen in \\( \\frac { 1 } { 2 } \\) of…

tanvi finds that her robot vacuum can clean her 150 - square - foot kitchen in \\( \\frac { 1 } { 2 } \\) of an hour. how many square feet could the robot vacuum clean in 1 hour? simplify your answer and write it as a proper fraction, mixed number, or whole number. square feet

tanvi finds that her robot vacuum can clean her 150 - square - foot kitchen in \\( \\frac { 1 } { 2 } \\) of an hour. how many square feet could the robot vacuum clean in 1 hour? simplify your answer and write it as a proper fraction, mixed number, or whole number. square feet

Answer

Explanation:

Step1: Analyze the relationship between time and area

We know that the robot vacuum cleans 150 square - feet in (\frac{1}{2}) hour. Let (x) be the area cleaned in 1 hour. Since the rate of cleaning is constant, we can set up a proportion. The rate (r=\frac{\text{Area}}{\text{Time}}). If (r_1 = r_2), and (r_1=\frac{150}{\frac{1}{2}}), (r_2=\frac{x}{1})

Step2: Calculate the area (x)

We use the formula (x = 150\div\frac{1}{2}). According to the rule of dividing by a fraction (a\div\frac{b}{c}=a\times\frac{c}{b}), so (150\div\frac{1}{2}=150\times2)

[150\times2 = 300]

Answer:

300