Two trains are running in opposite direction with the same speed. If the length of each train is 255 metres and they cross each other in 17 seconds, then what is the speed of each train?

When two trains move in opposite directions, the distance that must be covered for them to cross completely equals the sum of their lengths.

Total distance to be covered: $$255 \,\text{m} + 255 \,\text{m} = 510 \,\text{m}$$

The trains cross each other in $$17 \,\text{s}$$, so their relative speed is obtained from the basic formula $$\text{speed} = \frac{\text{distance}}{\text{time}}$$.

Relative speed $$= \frac{510}{17} \,\text{m/s} = 30 \,\text{m/s}$$

Because the trains move in opposite directions with the same speed, their relative speed is the sum of their individual speeds: $$v + v = 2v$$.

Thus, $$2v = 30 \,\text{m/s} \implies v = \frac{30}{2} = 15 \,\text{m/s}$$

Hence, the speed of each train is $$15 \,\text{m/s}$$.

Option C which is: 15 m/s