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blsea [12.9K]
3 years ago
6

You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s

ame amount of time upstream and downstream, travel down stream for 2400 m, but only one sixth that distance upstream. The current travels at a rate of 10 m/s. What is the time you spend rowing down stream? How fast would you be rolling in Stillwater?
Mathematics
1 answer:
fredd [130]3 years ago
3 0

Answer:

Time spent rowing down stream =100\ seconds

Speed of boat in still water =14\ ms^{-1}

Step-by-step explanation:

Let speed of boat in still water be = x\ ms^{-1}

Speed of current = 10\ ms^{-1}

Speed of boat down stream = \textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}

Distance rowed down stream = 2400 m

Time spent rowing down stream = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s

Speed of boat up stream = \textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}

Distance rowed up stream = \frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m

Time spent rowing up stream = \frac{Distance}{Speed}=\frac{400}{x-10}\ s

We know that,

\textrm{Time spent rowing down stream =Time spent rowing up stream}

So,

\frac{2400}{x+10}=\frac{400}{x-10}

Cross multiplying

2400(x-10)=400(x+10)

Dividing both sides by 400

\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}

6(x-10)=x+10

6x-60=x+10

Adding 60 to both sides.

6x-60+60=x+10+60

6x=x+70

Subtracting both sides by x

6x-x=x+70-x

5x=70

Dividing both sides by 5.

\frac{5x}{5}=\frac{70}{5}

∴ x=14

Speed of boat in still water =14\ ms^-1

Time spent rowing down stream =\frac{2400}{14+10}=\frac{2400}{24}=100\ s

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By stips please ........
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Answer:

6x + 3h

Step-by-step explanation:

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= 3(X+h)^2 - 3x^2 / h

= 3(x^2 + 2hx + h^2) - 3x^2 / h

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Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (ii) Find the coordinates of the midpoint o
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Answer:

m=-\frac{1}{6} \approx -0.1667

M=(1,\frac{17}{2} )=(1,8.5)

d=\sqrt{37} \approx 6.083

Step-by-step explanation:

(i) For two different points on a line, the slope m is defined as the difference on the y-axis divided by the difference on the x-axis:

m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}

Where:

(x_1,y_1)=(-2,9)\\\\(x_2 , y_2)=(4,8)

So:

m=\frac{8-9}{4-(-2)} =\frac{-1}{6} \approx -0.1667

(ii)

To find the coordinates of the midpoint, you can use the following formula:

M=(\frac{x_1+x_2}{2}  , \frac{y_1+y_2}{2} )

Therefore:

M=(\frac{-2+4}{2}  , \frac{9+8}{2} )=(\frac{2}{2}  , \frac{17}{2} ) =(1,8.5 )

(iii) The distance between two points is given by the following formula:

d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}  }

Hence:

d=\sqrt{(4-(-2))^{2}+(8-9)^{2}  } =\sqrt{(6)^{2}+(-1)^{2}  } =\sqrt{36+1} =\sqrt{37} \\\\d\approx 6.083

8 0
3 years ago
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