1. 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?
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By: anil on 05 May 2019 02.14 am
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), => $$d = (35 imes 1.4) + 280$$ = $$49 + 280 = 329$$ km
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