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A row team paddles 30 miles upstream in 2 hours and 30 miles downstream in 45 minutes. How fast can the row team paddle in still water? What is the rate of the current?

Respuesta :

frika

Answer:

Rate in still water = 27.5 mph

Current's rate = 12.5 mph

Step-by-step explanation:

Let

x mph = row team rate in still water

y mph = current's rate

Upstream:

Distance = 30 miles

Time = 2 hours

Rate = x - y mph

Then

[tex]30=2(x-y)[/tex]

Downstream:

Distance = 30 miles

Time = 45 minutes [tex]=\dfrac{3}{4}[/tex] hour

Rate = x + y mph

Then

[tex]30=\dfrac{3}{4}(x+y)[/tex]

From the first equation:

[tex]30=2(x-y)\Rightarrow 15=x-y[/tex]

From the second equation:

[tex]30=\dfrac{3}{4}(x+y)\Rightarrow 40=x+y[/tex]

Add these two equations:

[tex]15+40=x-y+x+y\\ \\2x=55\\ \\x=27.5\ mph[/tex]

Subtract these two equations:

[tex]40-15=x+y-(x-y)\\ \\25=x+y-x+y\\ \\2y=25\\ \\y=12.5\ mph[/tex]

adioabiola

The speed of the row team paddle is; 27.5miles per hour.

The speed rate of the current is; 12.5miles per hour

Relative speed;

The row team paddles 30 miles upstream in 2 hours; in essence, 15miles per hour

  • 15 = x -y

And 30 miles downstream in 45 minutes. In essence, 30 ÷ 3/4 = 40miles per hour.

  • 40 = x +y.

Where;

  • x = speed of paddle

  • y = rate of current.

By solving the equations simultaneously;

x = 27.5 miles per hour

and y = 12.5 miles per hour.

Read more on relative speed;

https://brainly.com/question/17228388

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