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guapka [62]
3 years ago
5

tomorrow joelle wants to travel a total of 4 miles by walking and running. she plans to run for 20 minutes at a rate of 6 miles

per hour. how many minutes should she's walk at a rate of 3 miles per hour to finish traveling the 4 miles?
Mathematics
1 answer:
serg [7]3 years ago
7 0

Answer:

40 minutes

Step-by-step explanation:

Joelle wants to run for 20 minutes at rate 6 miles per hour so the distance traveled in this duration will be calculated by multiplying speed and time(in hours).

So, distance traveled in 20 minutes = 6 \times \frac{20}{60} = 2 miles.

As Joelle have to travel total 4 miles, the distance remaining after 20 minutes of traveling = 4 - 2 = 2 miles.

Now she has to walk for the remaining distance i.e. 2 miles with a speed of 3 miles/hour.

The time required to travel 2 miles will be calculated by dividing distance with speed.

So, time required = \frac{2}{3} hours.

Thus time in minutes = \frac{2}{3}\times 60 = 40 minutes.

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7 0
3 years ago
You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o
anyanavicka [17]

Answer:

x =\dfrac{45 \sqrt{6}}{ 2}

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0

-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0

\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}

squaring both sides; we get

\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}

\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}

By cross multiplying; we get

49x^2 = 25(54^2+x^2)

49x^2 = 25 \times 54^2+ 25x^2

49x^2-25x^2 = 25 \times 54^2

24x^2 = 25 \times 54^2

x^2 = \dfrac{25 \times 54^2}{24}

x =\sqrt{ \dfrac{25 \times 54^2}{24}}

x =\dfrac{5 \times 54}{\sqrt{24}}

x =\dfrac{270}{\sqrt{4 \times 6}}

x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}

x =\dfrac{45 \sqrt{6}}{ 2}

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Answer:

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Step-by-step explanation:


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