Mathematics: Aman stands at a point a on the bank of a straight river, 3 mi wide. to reach point b, l = 9 mi downstream on the opposite bank, he first rows his boat to point p on the opposite bank and then walks the remaining distance x to b, as shown in the figure. he can row at a speed of 2 mi/h and walk at a speed of 5 mi/h. (a) find a function that models the time t needed for the trip. (b) where should he land so that he reaches b as soon as possible? (round your answer to two decimal places.)

Yea I need help with this to...

Aman stands at a point a on the bank of a straight

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skittlesarebae6035

09.01.2022

So...hmm notice the picture

we get distance AP by using the pythagorean theorem

now, AP is just rowing, and PB is walking
their rates are 2mph and 5mph respectively
so... let us apply those rates to those distances of AP and PB

$\bf \textit{distance}=AP+PB\to \sqrt{x^2-18x+90}+x\quad 
\begin{cases}
AP\ rate=2mph\\
PB\ rate=5mph
\end{cases}
\\\\
thus
\\\\
\textit{time it took in hours}=t=\cfrac{\sqrt{x^2-18x+90}\ mi}{\frac{2mi}{h}}+\cfrac{x\ mi}{\frac{5mi}{h}}
\\\\\\
t=\cfrac{\sqrt{x^2-18x+90}}{2}+\cfrac{x}{5}$

Aman stands at a point a on the bank of a straight river, 3 mi wide. to reach point b, l = 9 mi down

Aman stands at a point a on the bank of a straight river, 3 mi wide. to reach point b, l = 9 mi down

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