# 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.

Question:

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.

Solution:

Distance covered by the train = 300 km

We know that distance covered $(d)=\operatorname{speed}(s) \times \operatorname{time}(t)$

$\Rightarrow s \times t=300$

$\Rightarrow t=\frac{300}{s} \quad \ldots(\mathrm{i})$

Also, given that if the speed is increased by 5 km/h, time of travel gets reduced by 2 hours.

$\Rightarrow(s+5)(t-2)=300 \quad \ldots \ldots$ (ii)

Put the value of (i) in (ii), we get

$(s+5)\left(\frac{300}{s}-2\right)=300$

$(s+5)\left(\frac{300-2 s}{s}\right)=300$

$(s+5)(300-2 s)=300 s$

$300 s-2 s^{2}+1500-10 s=300 s$

$-2 s^{2}+1500-10 s=0$

$-s^{2}+750-5 s=0$

$s^{2}+5 s-750=0$

$s^{2}+30 s-25 s-750=0$

$s(s+30)-25(s+30)=0$

$(s-25)(s+30)=0$

$(s-25)=0$ or $(s+30)=0$

$s=25$ or $s=-30$

Ignore the negative value
Therefore, the original speed = 25 km/h