A man travels 420 kilometres in, partly by rail and partly by steamer. He spends 8 hours more time on steamer. If the velocity of the steamer is 35 km/hr and the velocity of rail is 65 km/hr, how much distance does he cover by steamer?

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

=> Distance covered by rail = $$(420 - d)$$ km

Let time taken on rail = $$t$$ hours and time taken on steamer = $$(t + 8)$$ hours

Speed of rail = 65 km/hr and speed of steamer = 35 km/hr

Using, speed = distance/time

For steamer, $$\frac{d}{t + 8} = 35$$

=> $$d = 35t + 280$$ --------------(i)

For rail, $$\frac{420 - d}{t} = 65$$

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

=> $$420 - (35t + 280) = 65t$$

=> $$420 - 280 = 65t + 35t = 100t$$

=> $$t = \frac{140}{100} = 1.4$$ hours

Substituting value of $$t$$ in equation (i), => $$d = (35 \times 1.4) + 280$$

= $$49 + 280 = 329$$ km