A and B are 15 km apart and when travelling towards each other meet after half an hour where as they meet two and a half hours later if they travel in the same direction. The faster of the two travels at the speed of :

Solution(By Examveda Team)

Let the speed of A be x km/hr and speed of B be y km/hr
So, According to the question,
$$\eqalign{ & \frac{{15}}{{x + y}} = \frac{1}{2} \cr & x + y = 30.....(i) \cr & {\text{And,}} \cr & \frac{{15}}{{x - y}} = \frac{5}{2} \cr & 5x - 5y = 30.....(ii) \cr} $$
Multiply equation (i) by 5 and add
\[\begin{gathered} 5x + 5y = 150 \hfill \\ 5x - 5y = \,\,\,30 \hfill \\ \overline {10x\,\,\,\,\,\,\,\,\, = 180\,\,} \hfill \\ \end{gathered} \]
$$\boxed{x = 18{\text{ km/hr}}}$$

And y = 30 - $$x$$
⇒ y = 30 -18
⇒ y = 12 km/hr
∴ The faster travels at the speed of 18 km/hr