A man can row 30 km upstream and 44 km downstream in 10 hrs. It is also known that he can row 40 km upstream and 55 km downstream in 13 hrs. Find the speed of the man in still water. (Boat & Stream)

প্রশ্নে বলা হচ্ছে, এক ব্যক্তি স্রোতের প্রতিকূলে 30km এবং স্রোতের অনুকূলে 44km যেতে 10 ঘণ্টা সময় নেয়। আবার স্রোতের প্রতিকূলে 40 kmph এবং অনুকূলে 50 kmph যেতে লোকটি 13 ঘণ্টা সময় নেয়। স্থির পানিতে লোকটির গতিবেগ কত?

Let, the man's upstream speed is x kmph

And the man's downstream speed is y kmph

$$\begin{gathered} So, \frac{30}{x} + \frac{44}{y} = 10 . . . . . . . . . . . . \left(i\right) \\ And \frac{40}{x} + \frac{55}{y} = 13 . . . . . . . . . . . . \left(ii\right) \\ Now, we assume that \frac{1}{x} = a and \frac{1}{y} =b \\ \therefore 30a + 44b = 10 . . . . . . . . . . . . \left(iii\right) \\ And 40a +55b = 13 . . . . . . . . . . . . \left(iv\right) \\ Now multiplying \left(iii\right) by 4 and \left(iv\right) by 3, we get \\ \frac{120a + 176b = 40 \\ 120a + 165b = 39}{(-) 11b=1} \\ \Rightarrow b = \frac{1}{11} \\ Now, putting the value of b in equation \left(iii\right), we get \\ 30a +44b = 10 \\ \Rightarrow 30a + 44 \times \frac{1}{11} = 10 \\ \Rightarrow 30a + 4 = 10 \\ \Rightarrow 30a = 10-4 = 6 \\ \therefore a = \frac{6}{30} = \frac{1}{5} \\ That mean\text{'}s \frac{1}{x} = \frac{1}{5} \\ \therefore x = 5 \\ And \frac{1}{y} = \frac{1}{11} \\ \therefore y = 11 \\ \therefore Man\text{'}s rate in still water = \frac{1}{2} \left(5+11\right) = \frac{16}{2} = 8kmph. \end{gathered}$$