Two trains P and Q start from stations S and T towards each other. Train P takes 4 hours 48 minutes and train Q takes 3 hours 20 minutes to reach T and S, respectively, after they meet. If the speed of train P is 45 km/h, what is the speed of train Q ?

54 km/h

Formula used :-

(\(\frac{Speed \;of \;train\; P}{Speed\; of\; train\; Q}\))^2 = \(\frac{After \;meeting \;each \;other\; time \;taken\; by \;train\; Q}{After \;meeting \;each \;other\; time \;taken\; by \;train\; P}\)

4 hours 48 minutes = \(\frac{24}{5}\) hours

3 hours 20 minutes = \(\frac{10}{3}\) hours

Let the speed of Q be A  km/hr

(\(\frac{45}{A}\))² = \(\frac{10 × 5}{24×3 }\)

(\(\frac{45}{A}\))2 = \(\frac{25}{36 }\)

\(\frac{45}{A}\) = \(\frac{5}{6 }\)

A = 45 × \(\frac{6}{5 }\)

A = 54 km/hr

So , The speed of Q is 54 km/hr.