Question

A train covers a distance of $270km$ at a uniform speed. Had the speed been $15km/hour$ more, it would have taken one and a half hours to cover the same distance. Find the original speed of the train.

Answer 1

Step 1

Original speed of train$=90/xkm/hr$

Increased speed of train $=90/(x+15)km/hr$

Step 2

Given,

$$\begin{gathered} (90/x)–(90/x+15)=1/2 \\ {x}^2+15x–2700=0 \\ {x}^2+60x–45x–2700=0 \\ x(x+60)–45(x+60)=0 \\ (x+60)(x–45)=0 \\ \Rightarrow x=–60(notpossible) \\ x=45km/hr \end{gathered}$$

Hence, $45km/hr$ is the Original speed of train.