A man travels 401 kilometres in, partly by rail and partly by steamer. He spends 6 hours more time on steamer. If the velocity of the steamer is 21 km/hr and the velocity of rail is 56 km/hr, how much distance does he cover by steamer?

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

=> Distance covered by rail = $$(401 - d)$$ km

Let time taken on rail = $$t$$ hours and time taken on steamer = $$(t + 6)$$ hours

Speed of rail = 56 km/hr and speed of steamer = 21 km/hr

Using, speed = distance/time

For steamer, $$\frac{d}{t + 6} = 21$$

=> $$d = 21t + 126$$ --------------(i)

For rail, $$\frac{401 - d}{t} = 56$$

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

=> $$401 - (21t + 126) = 56t$$

=> $$401 - 126 = 56t + 21t = 77t$$

=> $$t = \frac{275}{77} = \frac{25}{7}$$ hours

Substituting value of $$t$$ in equation (i), => $$d = (21 \times \frac{25}{7}) + 126$$

= $$(3 \times 25) + 126 = 75 + 126 = 201$$ km