A man travels 800 km in partly by rail and partly by steamer. He spends 7 hours more time on steamer. If the velocity of the steamer is 20 km/hr and the velocity of rail is 55 km/hr, how much distance does he cover by steamer?

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

=> Distance covered by rail = $$(800 - d)$$ km

Let time taken on rail = $$t$$ hours and time taken on steamer = $$(t + 7)$$ hours

Speed of rail = 55 km/hr and speed of steamer = 20 km/hr

Using, speed = distance/time

For steamer, $$\frac{d}{t + 7} = 20$$

=> $$d = 20t + 140$$ --------------(i)

For rail, $$\frac{800 - d}{t} = 55$$

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

=> $$800 - (20t + 140) = 55t$$

=> $$800 - 140 = 55t + 20t = 75t$$

=> $$t = \frac{660}{75} = 8.8$$ hours

Substituting value of $$t$$ in equation (i), => $$d = (20 \times 8.8) + 140$$

= $$176 + 140 = 316$$ km