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3 years ago

Bill hikes 8 miles in 3 hours. At this rate. how many miles will he hike after 2 hours?

Mathematics

2 answers:

kompoz [17]3 years ago

8 0

Answer: $5 \frac{1}{3}$ miles

For the rate of 8 miles in 3 hours, you divide.

For the rate of - miles in 2 hours, multiply.

8 x 2 = 3x

16 = 3x

Now, we have to divide by 3x by 3.

3x divided by 3 = 5 1/3

Answer = 5 1/3

exis [7]3 years ago

6 0

Answer:

5 1/3 miles

Step-by-step explanation:

We can use a ratio to solve

8 miles x miles

------------ = --------

3 hours 2 hours

Using cross products

8*2 = 3x

16 = 3x

Divide by 3

16/3 = 3x/3

5 1/3 miles =x

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Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

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The equation of a line:

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substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

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Convert the equation:

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$\dfrac{2}{3}x-y+b=0$ |multiply both sides by 3

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

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substitute:

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$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

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$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |divide both sides by 3

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

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