1. 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?
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By: anil on 05 May 2019 02.11 am
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), => $$d = (21 imes frac{25}{7}) + 126$$ = $$(3 imes 25) + 126 = 75 + 126 = 201$$ km
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