question_answer

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/ hour, it takes 2 hours less in the journey. Find the original speed of the train.

Answer:

Let original speed of train \[=x\text{ }km/hr.\]

Increased speed of train \[=(x+5)\text{ }km/hr.\]

Distance \[=300\text{ }km\]

According to the question,

\[\frac{300}{x}-\frac{300}{x+5}=2\]

\[\frac{300(x+5-x)}{(x)(x+5)}=2\]

\[1500=2\left( {{x}^{2}}+5x \right)\]

\[1500=2{{x}^{2}}+10x\]

\[2{{x}^{2}}+10x-1500=0\]

\[{{x}^{2}}+5x-750=0\]

\[{{x}^{2}}+30x-25x-750=0\]

\[x(x+30)-25(x+30)=0\]

\[(x+30)(x-25)=0\]

Either \[x+30=0\] or \[x-25=0\]

\[\Rightarrow \]                    \[x=-30\] (Rejected), so \[x=25\]

Original speed of train is \[25\text{ }km/hr.\]