Question

A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than o return to the same spot. Find the speed of the stream.

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{Let the speed of the stream be}x\text{km/hr.}\end{array} \\ \mathrm{Given}: \\ \mathrm{Speed}\mathrm{of}\mathrm{the}\mathrm{boat}=18\mathrm{km}/\mathrm{hr} \\ \therefore \text{Speed downstream =}(18+x)\text{km/hr} \\ \mathrm{S}\text{peed upstream =}(18-x)\text{km/hr} \\ \therefore \frac{24}{(18-x)}-\frac{24}{(18+x)}=1 \\ \Rightarrow \frac{1}{(18-x)}-\frac{1}{(18+x)}=\frac{1}{24} \\ \Rightarrow \frac{18+x-18+x}{(18-x)(18+x)}=\frac{1}{24} \\ \Rightarrow \frac{2x}{{18}^2-x^2}=\frac{1}{24} \\ \Rightarrow 324-x^2=48x \\ \Rightarrow 324-x^2-48x=0 \\ \Rightarrow x^2+48x-324=0 \\ \Rightarrow x^2+(54-6)x-324=0 \\ \Rightarrow x^2+54x-6x-324=0 \\ \Rightarrow x(x+54)-6(x+54)=0 \\ \Rightarrow (x+54)(x-6)=0 \\ \Rightarrow x=-54\text{or}x=6 \\ \text{The value of}x\text{cannot be negative; thereore, the speed of the stream is 6 km/hr.} \end{gathered}$$