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3 years ago

If I can paint 96 sq ft in 15 minutes how long does it take to paint 1 sq ft

Mathematics

1 answer:

White raven [17]3 years ago

8 0

It takes 0.15625 minutes to paint 1 square feet

Solution:

Given that, I can paint 96 sq ft in 15 minutes

To find: Time taken to paint 1 square feet

From given,

96 square feet is painted in 15 minutes

Let "x" be the time taken to paint 1 square feet

Then, we can say,

96 square feet = 15 minutes

1 square feet = x minutes

This forms a proportion and we can solve the sum by cross multiplying

$96 \times x = 15 \times 1\\\\x = \frac{15}{96}\\\\x = 0.15625$

Thus it takes 0.15625 minutes to paint 1 square feet

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Step-by-step explanation:

First we define two generic vectors in our $\mathbb{R}^2$ space:

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As second condition we have that:

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Which is the same:

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$\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}$

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Remembering,

$y_1=-3x_1\\y_2=-3x_2$

The two vectors we are looking for are:

$v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})$

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