A man travels 400 km in, partly by rail and partly by steamer. He spends 9 hours more time on steamer. If the velocity of the steamer is 30 km/hr and the velocity of rail is 70 km/hr, how much distance does he cover by steamer?

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

=> Distance covered by rail = $$(400 - d)$$ km

Let time taken on rail = $$t$$ hours and time taken on steamer = $$(t + 9)$$ hours

Speed of rail = 70 km/hr and speed of steamer = 30 km/hr

Using, speed = distance/time

For steamer, $$\frac{d}{t + 9} = 30$$

=> $$d = 30t + 270$$ --------------(i)

For rail, $$\frac{400 - d}{t} = 70$$

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

=> $$400 - (30t + 270) = 70t$$

=> $$400 - 270 = 70t + 30t = 100t$$

=> $$t = \frac{130}{100} = 1.3$$ hours

Substituting value of $$t$$ in equation (i), => $$d = (30 \times 1.3) + 270$$

= $$39 + 270 = 309$$ km