Question

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 kmph less than that of the faster train, find the speeds of two trains.

Answer 1

Let the speed of faster train be x km/h.
Then, the speed of slower train is (x − 10) km/h.

Given:
A faster train takes one hour less than a slower train for a journey of 200 km.

$\frac{\mathrm{Distance}}{\mathrm{Speed}}=\mathrm{Time}$

Time taken by faster train to cover 200 km = $\frac{200}{x}$ h
Time taken by slower train to cover 200 km = $\frac{200}{x-10}$ h

According to the question,

$$\begin{gathered} \frac{200}{x-10}-\frac{200}{x}=1 \\ \Rightarrow \frac{200\left(x\right)-200\left(x-10\right)}{\left(x\right)\left(x-10\right)}=1 \\ \Rightarrow \frac{200x-200x+2000}{x^2-10x}=1 \\ \Rightarrow 2000=x^2-10x \\ \Rightarrow x^2-10x-2000=0 \\ \Rightarrow x^2-50x+40x-2000=0 \\ \Rightarrow x\left(x-50\right)+40\left(x-50\right)=0 \\ \Rightarrow \left(x-50\right)\left(x+40\right)=0 \\ \Rightarrow x=50,-40 \\ \mathrm{But}\left(x\right)\mathrm{is}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{train},\mathrm{which}\mathrm{is}\mathrm{always}\mathrm{positive}. \\ \mathrm{Thus},x=50 \end{gathered}$$
and x − 10 = 40

Hence, the speed of fast train is 50 km/h and the speed of slow train is 40 km/h.