Question

A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.

Answer 1

Let the speed of the fast train bethen

the speed of the slow train be

Time taken by the fast train to cover

Time taken by the slow train to cover

Therefore,

$$\begin{gathered} \frac{200}{\left(x-10\right)}-\frac{200}{x}=1 \\ \Rightarrow \frac{200x-200\left(x-10\right)}{x\left(x-10\right)}=1 \\ \Rightarrow \frac{200x-220x+2000}{x^2-10x}=1 \\ \Rightarrow x^2-10x=2000 \\ \Rightarrow x^2-10x-2000=0 \end{gathered}$$

$$\begin{gathered} \Rightarrow x^2-50x+40x-2000=0 \\ \Rightarrow x\left(x-50\right)+40\left(x-50\right)=0 \\ \Rightarrow \left(x-50\right)\left(x+40\right)=0 \end{gathered}$$

So, either

Or

But, the speed of the train can never be negative.

Thus, when then

Hence, the speed of the fast train is

and the speed of the slow train is respectively.