Question

A train takes $2hours$ less for a journey of $300km$, if its speed is increased by $5km/h$ from its usual speed. Find the usual speed of the train.

Answer 1

Distance = $300km$

Let speed be $v$

Let time taken usually be $t$

We know, $Speed=\frac{Distance}{Time}$

Usual Speed is $v=\frac{300}{t}..........\left(1\right)$

When speed is increased $v+5=\frac{300}{t-2}.........\left(2\right)$

From (1) and (2)

$v+5=\frac{300}{\frac{300}{v}-2}\Rightarrow (v+5)(300-2v)=300v\Rightarrow 300v-2v^2+1500-10v=300v\Rightarrow 2v^2+10v-1500=0\Rightarrow v=25,-30$

v cannot be negative so $v=25km/h$