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ankoles [38]
2 years ago
12

Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minut

es. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Choose the most logical value for the variable to represent.
Let x = .

3m = 15

9 + 15m = 12m – 1

3m = 18

9 + 6 – 15 = 15m – 12m
Mathematics
1 answer:
never [62]2 years ago
5 0

By solving a system of equations, we conclude that Kelli's speed on still water is 6.1km/h

<h3></h3><h3>How fast can Kelli swim in still water?</h3>

Let's say that the speed of Kelli in still water is S. And we know that the speed of the river is 5km/h.

When she swims upstream, her velocity is:

(S - 5km/h)

When she swims downstream, her velocity is:

(S + 5km/h)

With the given information, we can write for a distance D:

(S - 5km/h)*1h = D

(S + 5km/h)*6min = D

First, let's rewrite 6 minutes into hours.

1 hour = 60min

6 min = 6/(60) hours = 0.1 hours

Then the system of equations that we need to solve is:

(S - 5km/h)*1h = D

(S + 5km/h)*0.1h = D

D is the same distance in both cases, then we can write:

(S - 5km/h)*1h = (S + 5km/h)*0.1h

Now we can solve this for S.

S*1h - 5km = S*0.1h + 0.5km

S*1h - S*0.1h = 5km + 0.5km

S*(0.9h) = 5.5km

S = 5.5km/0.9h = 6.1km/h

Kelli's speed on still water is 6.1km/h

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

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Match the following rational expressions to their rewritten forms.
Nookie1986 [14]

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}

And the rewritten forms:

(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}

So, correct option is 3.

(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}

So, correct option is 1.

(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}

So, correct option is 2.

(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}

So, correct option is 4.

The answer is also attached in the answer area.

7 0
2 years ago
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