Question

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3hours$ more to cover the same distance. Find the speed of the train.

Answer 1

Step 1: Find time taken for the journey

Let the speed of the train be$xkmph$

Time taken for the journey $=\frac{480}{x}$

Given speed is decreased by$8kmph$

Hence the new speed of train$=(x–8)kmph$

Time taken for the journey $=\frac{480}{(x–8)}$

Step 2: Find the speed of the train

Now according to question

$$\begin{gathered} \frac{480}{(x–8)}–\frac{480}{x}=3 \\ \Rightarrow \frac{480(x–x+8)}{x(x-8)}=3 \\ \Rightarrow \frac{480}{3}\times 8=x^2-8x \\ \Rightarrow 1280=x^2–8x \\ {x}^2–8x–1280=0 \end{gathered}$$

On solving we get$x=40$

Hence, the speed of train is $40kmph$.