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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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Step-by-step explanation:

Given,

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Let,

x represent the number of adult tickets sold

y represent the number of child tickets sold

According to given statement;

x+y=548             Eqn 1

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Multiplying Eqn 1 by 6.50

6.50(x+y=548)\\6.50x+6.50y=3562\ \ \ Eqn\ 3

Subtracting Eqn 2 from Eqn 3

(6.50x+6.50y)-(6.50x-3.50y)=3562-2881\\6.50x+6.50y-6.50x-3.50y=681\\3y=681

Dividing both sides by 3

\frac{3y}{3}=\frac{681}{3}\\y=227

Putting y=227 in Eqn 1

x+227=548\\x=548-227\\x=321

Regal theater sold 321 adult tickets and 227 children tickets.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/1289682
  • brainly.com/question/12932203

#LearnwithBrainly

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Answer:

← SOLUTION →

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6

[ but 2x-1 = {2 × 1

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<u>hope</u><u> it's</u><u> helpful</u><u> to</u><u> </u><u>you </u><u>good</u><u> </u><u>luck</u><u> </u><u>for </u><u>study</u>

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