A train $105\text{ metres}$ long travels at $60\text{km/hr}$. How long does it take to cross another train $175\text{ metres}$ long, running at $54\text{km/hr}$ in the same direction?

Total distance to be covered when crossing each other = Sum of the lengths of both trains
$$\text{Distance}=105\text{m}+175\text{m}=280\text{m}$$

Since the trains are moving in the same direction, their relative speed is the difference of their speeds:

$$\text{Relative Speed}=60\text{km/hr}-54\text{km/hr}=6\text{km/hr}$$

Convert relative speed into $\text{m/s}$:

$$\text{Relative Speed}=6\times \frac{5}{18}\text{m/s}=\frac{5}{3}\text{m/s}$$

Time taken to cross each other:

$$\text{Time}=\frac{\text{Distance}}{\text{Relative Speed}}=\frac{280}{\frac{5}{3}}=\frac{280\times 3}{5}=56\times 3=168\text{seconds}$$

Convert seconds into minutes and seconds:

$$168\text{seconds}=2\text{minutes and }48\text{seconds}$$