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While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels

taurus [48]

Part 1: The speed of the boat traveling downstream is $(18+w)$ miles per hr.

The speed of the boat traveling upstream is $(18-w)$ miles per hr.

Part 2: The speed of the current is 4 miles per hour.

Explanation:

Part (1): The motorboat travels 18 miles per hour in still.

Let w represents the speed of the current.

When the boat travels downstream, the speed of the current will get added to the speed of the boat.

Thus, the expression can be written as $(18+w)$ miles per hr

Hence, the speed of the boat traveling downstream is $(18+w)$ miles per hr.

When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.

Thus, the expression can be written as $(18-w)$ miles per hr.

Hence, the speed of the boat traveling upstream is $(18-w)$ miles per hr.

Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.

The distance formula is given by $distance $=$ speed $\times$ time$

Substituting, we have,

$49=(18-w)t\\49=18t-wt$ ---------------(1)

$77=(18+w)t\\77=18t+wt$ ---------------(2)

Solving using elimination method,

$49=18 t-w t\\77=18 t+w t\\-------\\126=36t$

Dividing both sides by 36, we have,

$t=3.5$

Substituting $t=3.5$ in $49=18 t-w t$ , we get,

$49=18(3.5)-w (3.5)\\$

$49=63-3.5w\\$

$-14=-3.5w\\$

$4=w$

Thus, the speed of the current is $w=4$ miles per hour.

5 0

4 years ago

Classify the system of equations 2x + y - 7 = 0 1/3 x + y - 4 = 0

KATRIN_1 [288]

Answer:

B

Step-by-step explanation:

The equations are:

2x + y - 7 = 0

and

1/3x + y -4 = 0

Let's rearrange the first to get:

y = -2x + 7

Putting this into the 2nd equation we get:

$\frac{1}{3}x + y -4 = 0\\\frac{1}{3}x + (-2x+7) -4 = 0\\\frac{1}{3}x-2x+7-4=0\\\frac{5}{3}x=3\\x=\frac{9}{5}$

Now, y would be:

$y=-2x+7\\y=-2(\frac{9}{5})+7\\y=3\frac{2}{5}$

Solving the equation we see that there is 1 unique solution with 1 x value and another y values. That means, when graphing, the lines would intersect.

Answer choice B is right.

<u>Note:</u> Coincident means the same line and parallel means there would be no solution when solving

3 0

3 years ago

Which of the following is the point and slope of the equation y + 2 = 2(x - 8)?

vaieri [72.5K]

I think it would be (2,-8),2

7 0

3 years ago

Irrational numbers can never be precisely represented in decimal form, why is this?

tatyana61 [14]

Because most of them keep on going for infinite. For example, $\pi$ is an irrational number that goes on forever 3.14159 etc etc etc

3 0

3 years ago

the length and width of a rectangle are whole numbers of centimeters. neither is divide by 6.the area of the rectangle is 36 squ

liraira [26]

Note that

36=1·36;
36=2·18;
36=3·12;
36=4·9;
36=6·6.

If neither (length and width) is divide by 6, then cases 1, 2, 3 and 5 are extra, because

36:6=6 (is divide by 6);
18:6=3 (is divide by 6);
12:6=2 (is divide by 6);
6:6=1 (is divide by 6).

The only possible dimensions are: width - 4 cm and length - 9 cm.

Then the perimeter is

$P=4+9+4+9=26$ cm.

Answer: 26 cm.

3 0

3 years ago