If a train crosses a pole in $15\text{seconds}$, how long will it take for the train, travelling at a speed of $90\text{km/hr}$, to cross a bridge that is $600\text{meters}$ long?

First, convert the train's speed from $\text{km/hr}$ to $\text{m/s}$:
$$\text{Speed}=90\times \frac{5}{18}=5\times 5=25\text{m/s}$$

When a train crosses a pole, the distance covered is equal to the length of the train ($L$).

$$\text{Length of the train }(L)=\text{Speed}\times \text{Time}=25\text{m/s}\times 15\text{s}=375\text{meters}$$

When the train crosses a $600\text{meters}$ long bridge, the total distance to be covered is:

$$\text{Total Distance}=\text{Length of train}+\text{Length of bridge}=375+600=975\text{meters}$$

Time taken to cross the bridge:

$$\text{Time}=\frac{\text{Total Distance}}{\text{Speed}}=\frac{975}{25}=39\text{seconds}$$