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A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

Nat2105 [25]

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

$\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}$

We know, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

According to the question,

$\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}$

Taking LCM and 6 common

$6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}$

Take 6 to another side,

$\frac{9}{9x-x^2}=\frac{8}{3\times 6}$

Cross multiply,

$9\times 18=8\times(9x-x^2)$

$162=72x-8x^2$

Taking 4 common and cancel out

$4x^2-36x+81=0$

Solve quadratic equation by middle term split,

$4x^2-18x-18x+81=0$

$2x(2x-9)-9(2x-9)=0$

$(2x-9)(2x-9)=0$

$\Rightarrow 2x-9=0$

$\Rightarrow x=\frac{9}{2}=4.5$

Therefore, The speed of the river's current is 4.5 km/hr.

6 0

3 years ago

Madison is carrying a 11.3 liter jug of sports drink that weighs 7 kg.

stellarik [79]

Answer:

$\large\boxed{\large\boxed{constat\text{ }multiple=\frac{113liter}{70kg}}}$

Explanation:

The constant multiple of liters in a jug to the weight in kilograms is the ratio or fraction that represents the number of liters of the sports drink in a jug to the weight.

$constat\text{ }multiple=ratio=\frac{number\text{ }of\text{ }liters}{weight\text{ }in\text{ }kg}$

$constat\text{ }multiple=\frac{11.3liter}{7kg}$

Convert the fraction into an equivalent fraction with integer numbers:

$constat\text{ }multiple=\frac{11.3liter\times 10}{7kg\times 10}=\frac{113liter}{70kg}$

Since, the fraction cannot be reduced, that is the answer.

6 0

3 years ago

What is the value of x if the average of 10, 11, 12 and x is 9?

frosja888 [35]

Answer: The value of x is 3.

Step-by-step explanation:

Since we have given that

10,11, 12 and x

Average of above numbers = 9

As we know that

Average is given by

$\dfrac{\text{Sum of observation}}{\text{Number of observation}}\\\\\\\dfrac{10+11+12+x}{4}=9\\\\10+11+12+x=9\times 4\\\\33+x=36\\\\x=36-33\\\\x=3$

Hence, the value of x is 3.

6 0

3 years ago

How to compare 2 5/9 and 21/3

max2010maxim [7]

Answer:

2 5/9 is less than 21/3; 2 5/9 < 21/3

Step-by-step explanation:

Step 1: Convert 2 5/9 into an improper fraction

2 5/9 = 2 * 9/9 + 5/9 = 18/9 + 5/9 = 23/9

Step 2: Convert 21/3 so the denominator is 9

21*3 / 3*3 = 63/9

Step 3: Compare

23/9 < 63/9

Answer: 2 5/9 is less than 21/3; 2 5/9 < 21/3

5 0

3 years ago

Read 2 more answers

Help please this my little brother work

masha68 [24]

Huh? What do you mean I don't understand

7 0

3 years ago

Read 2 more answers