Question

The distance between the two stations was $550km$. Two trains start at same time from the two station on parallel track to cross one another .The speed of one train is $10km$ per hour more than the other . If after $3$ hours the train reaches $40km$, find their speed?

Answer 1

Let the trains be $A$ and $B$.

Speed of train $A=xkm/h$

Speed of train $B=(x+10)km/h$

Since, the $\text{Distance}=\text{Speed}\times \text{Time}$

So, after $3$ hours,

distance travelled by train $A=3xkm$

distance travelled by train $B=3(x+10)km$

Now distance between them is $40km$

So $3x+3(x+10)=550-40$

$\Rightarrow 3x+3x+30=510$

$\Rightarrow 6x+70=510$

$\Rightarrow 6x=550–70$

$\Rightarrow 6x=480$

$\Rightarrow x=\frac{480}{6}$

$\Rightarrow x=80$---(1)

$\Rightarrow x+10=80+10=90$

Therefore, Speed of train $A=80km/h$

Speed of train $A=(80+10)km/h=90km/h$