A man travels 404 kilometres in partly by rail and steamer. He spends 10 hours more time on steamer. If the speed of the steamer is 30 km/hr and the velocity of rail is 50 km/hr, how much distance does he cover by steamer?

Let distance covered by steamer = $$d$$ km

=> Distance covered by rail = $$(404 - d)$$ km

Let time taken on rail = $$t$$ hours and time taken on steamer = $$(t + 10)$$ hours

Speed of rail = 50 km/hr and speed of steamer = 30 km/hr

Using, speed = distance/time

For steamer, $$\frac{d}{t + 10} = 30$$

=> $$d = 30t + 300$$ --------------(i)

For rail, $$\frac{404 - d}{t} = 50$$

Substituting value of $$d$$ from equation (i), we get :

=> $$404 - (30t + 300) = 50t$$

=> $$404 - 300 = 50t + 30t = 80t$$

=> $$t = \frac{104}{80} = 1.3$$ hours

Substituting value of $$t$$ in equation (i), => $$d = (30 \times 1.3) + 300$$

= $$39 + 300 = 339$$ km