: প্রশ্নে বলা হচ্ছে, এক ব্যক্তি স্রোতের অনুকূলে 28km পথ যেয়ে পুনরায় ফিলে আসলো। যেতে যে সময় লেগেছিল। ফিরে আসতে তার দ্বিগুণ সময় লাগল। স্রোতের বেগ দ্বিগুণ হলে ঐ দূরত্ব স্রোতের অনুকূলে যেয়ে পুনরায় ফিরে আসতে মোট 672 মিনিট সময় লাগে । স্থির পানিতে নৌকার বেগ ও স্রোতের বেগ কত?

Let, the speed of boat in still water be x kmph and the speed of stream in still water be y kmph.

∴ The boat's downstream speed will be (x + y)

and the boat's upstream speed will be (x − y)

According to question,

$$\begin{gathered} 2 \left(\frac{28}{x+y}\right) = \frac{28}{x-y} \\ \Rightarrow \frac{2}{x+y} = \frac{1}{x-y} [Dividing both sides by 28] \\ \Rightarrow 2x -2y = x+y \\ \Rightarrow 2x - x = y + 2y = 3y \\ \therefore x = 3y \end{gathered}$$

Now, total time taken by the boat (if the stream gets 2 times high) to go and come back $= \frac{672}{60} = \frac{56}{5} hours$

So, according to the question

$$\begin{gathered} \frac{28}{x+2y} + \frac{28}{x-2y} = \frac{56}{5} [As, the speed of the stream is two times the speed of boat] \\ \Rightarrow \frac{28}{3y + 2y} + \frac{28}{3y - 2y} = \frac{56}{5} \\ \Rightarrow 28 \left(\frac{1}{5y} + \frac{1}{y}\right) = \frac{56}{5} \\ \Rightarrow \frac{1}{5y} + \frac{1}{y} = \frac{2}{5} \\ \Rightarrow \frac{1+5}{5y} = \frac{2}{5} \\ \Rightarrow \frac{6}{5y} = \frac{2}{5} \\ \Rightarrow 10y =30 \\ \therefore y = \frac{30}{10} = 3 kmph \\ Now, by putting the value of y in equation \left(i\right), we get \\ x=3y \\ \Rightarrow x = 3 \times 3 = 9 kmph \\ \therefore Speed of the boat in still water is 9 kmph and speed of the stream in still water is 3 kmph. \end{gathered}$$