1. 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?
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By: anil on 05 May 2019 02.11 am
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), => $$d = (20 imes 8.8) + 140$$ = $$176 + 140 = 316$$ km
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