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Sever21 [200]
3 years ago
14

Petes boat can travel 48 miles upstream in 4 hours. The return trip takes 3 hours. Find the speed of the boat in still water and

the speed of the current.
Mathematics
1 answer:
tankabanditka [31]3 years ago
5 0
So... hmm bear in mind, when the boat goes upstream, it goes against the stream, so, if the boat has speed rate of say "b", and the stream has a rate of "r", then the speed going up is b - r, the boat's rate minus the streams, because the stream is subtracting speed as it goes up

going downstream is a bit different, the stream speed is "added" to boat's
so the boat is really going faster, is going b + r

notice, the distance is the same, upstream as well as downstream
thus   \bf \begin{cases}
b=\textit{rate of the boat}\\
r=\textit{rate of the river}
\end{cases}\qquad thus
\\\\\\

\begin{array}{lccclll}
&distance&rate&time(hrs)\\
&----&----&----\\
upstream&48&b-r&4\\
downstream&48&b+4&3
\end{array}
\\\\\\

\begin{cases}
48=(b-r)(4)\to 48=4b-4r\\\\
\frac{48-4b}{-4}=r\\
--------------\\
48=(b+r)(3)\\
-----------------------------\\\\
thus\\\\
48=\left[ b+\left(\boxed{\frac{48-4b}{-4}}\right) \right] (3)
\end{cases}

solve for "r", to see what the stream's rate is

what about the boat's? well, just plug the value for "r" on either equation and solve for "b"
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The reasonable estimate for the length of side DE is 3 units

Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.

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2 years ago
Please help, I can't figure out how to set this up. There's supposed to be 2 equations.
Valentin [98]

Hello from MrBillDoesMath

Answer:     + 4/7,   6 (13/14)

Discussion:

Let L be the larger of the two numbers and S the smaller of the two. Then the first sentence translates into this:


-6L - L = -4  =>

-7L = -4        =>          (divide both sides by -7)

L = - (-4)/(-7) = + 4/7       (*)


The second sentence translates to

2 (L + S) = 15  =>               (divide both sides by 2)

(L +S) = 15/2  =>                (subtract L from each side)

S = 15/2 - L = 15/2 - 4/7    (using (*) above)

So

S = 15*7/(2*7) - (4*2)/(7*2)       (combine over common denominator of 14)

S = 105/14 - 8/14 = 97/14 = 6 13/14

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Thank you,

Mr. B


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3 years ago
How far have u gone if you go 50 miles per hour for 30 seconds
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divide amount of miles with 3600 seconds

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0.01389 (rounded) miles is your answer

hope this helps
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3 years ago
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Problem 13

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This is known as the box method to keep track of all the terms multiplied.

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