Question

A train travels a distance of 360 km at a uniform speed. If the speed of he train is increased by 5 km an hour, the journey would have taken 1 hour less. Find the original speed of the train.

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{Let the original speed of the train be}x\text{km/hr}\text{.}\end{array} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \frac{360}{x}-\frac{360}{(x+5)}=1 \\ \Rightarrow \frac{360(x+5)-360x}{x(x+5)}=1 \\ \Rightarrow \frac{360x+1800-360x}{x^2+5x}=1 \\ \Rightarrow 1800=x^2+5x \\ \Rightarrow x^2+5x-1800=0 \\ \Rightarrow x^2+(45-40)x-1800=0 \\ \Rightarrow x^2+45x-40x-1800=0 \\ \Rightarrow x(x+45)-40(x+45)=0 \\ \Rightarrow (x+45)(x-40)=0 \\ \Rightarrow x=-45\text{or}x=40 \\ \mathrm{Th}\text{e speed of train cannot be negative; therefore, the speed is 40 km/hr.} \end{gathered}$$