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Home » The speed of a boat in still water is . It can go upstream and downstream is 5 hours. Fid the speed of the stream
The speed of a boat in still water is 8 \mathrm{~km} / \mathrm{hr}. It can go 15 \mathrm{~km} upstream and 22 \mathrm{~km} downstream is 5 hours. Fid the speed of the stream
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
The speed of a boat in still water is 8 \mathrm{~km} / \mathrm{hr}. It can go 15 \mathrm{~km} upstream and 22 \mathrm{~km} downstream is 5 hours. Fid the speed of the stream

Speed of the boat in still water =8 \mathrm{~km} / \mathrm{hr}.

Let the speed of the stream be x \mathrm{~km} / \mathrm{hr}.

\therefore Speed upstream =(8-x) \mathrm{km} / \mathrm{hr}

Speed downstream =(8+x) \mathrm{km} / \mathrm{hr}

Speed downstream =(8+x) \mathrm{km} / \mathrm{hr} . Time taken to go 22 \mathrm{~km} downstream =\frac{22}{(8+x)} h r

Time taken to go 15 \mathrm{~km} upstream =\frac{15}{(8-x)} h r

According to the question:

\begin{array}{l} \Rightarrow \frac{22}{(8+x)}+\frac{15}{(8-x)}=5 \\ \Rightarrow \frac{22}{(8+x)}+\frac{15}{(8-x)}-5=0 \end{array}
\begin{array}{l} \Rightarrow \frac{22(8-x)+15(8+x)-5(8-x)(8+x)}{(8-x)(8+x)}=0 \\ \Rightarrow 176-22 x+120+15 x-320+5 x^{2}=0 \\ \Rightarrow 5 x^{2}-7 x-24=0 \\ \Rightarrow 5 x^{2}-(15-8) x-24=0 \\ \Rightarrow 5 x^{2}-15 x+8 x-24=0 \\ \Rightarrow 5 x(x-3)-8(x-3)=0 \\ \Rightarrow(x-3)(5 x-8)=0 \\ \Rightarrow x-3=0 \text { or } 5 x-8=0 \\ \Rightarrow x=3 \text { or } x=\frac{8}{5} \\ \Rightarrow x=3 \quad(\because \text { Speed cannot be a fraction }) \\ \therefore \text { Speed of the stream }=3 \mathrm{~km} / \mathrm{hr} \end{array}

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