1. One third of a certain journey is covered at the speed of 80 km/hr, one fourth of the journey at the speed of 50 km/hr And the rest at the speed of 100 km/hr, what will be the average speed (in km/hr) for the whole journey ?
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By: anil on 05 May 2019 02.27 am
Let the total distance = $$12x$$ km Distance covered at 80 km/hr = $$frac{12x}{3}=4x$$ km => Time taken = $$frac{4x}{80}=frac{x}{20}$$ hours Distance covered at 50 km/hr = $$frac{12x}{4}=3x$$ km
=> Time taken = $$frac{3x}{50}$$ hours
Distance covered at 100 km/hr = $$12x-4x-3x=5x$$ km
=> Time taken = $$frac{5x}{100}=frac{x}{20}$$ hours
Thus, total time = $$frac{x}{20}+frac{3x}{50}+frac{x}{20}$$ = $$frac{x}{10}+frac{3x}{50}=frac{8x}{50}$$ $$ herefore$$ Average speed = total distance/total time = $$frac{12x}{frac{8x}{50}}$$ = $$12 imesfrac{50}{8}=75$$ km/hr => Ans - (A)
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=> Time taken = $$frac{3x}{50}$$ hours
Distance covered at 100 km/hr = $$12x-4x-3x=5x$$ km
=> Time taken = $$frac{5x}{100}=frac{x}{20}$$ hours
Thus, total time = $$frac{x}{20}+frac{3x}{50}+frac{x}{20}$$ = $$frac{x}{10}+frac{3x}{50}=frac{8x}{50}$$ $$ herefore$$ Average speed = total distance/total time = $$frac{12x}{frac{8x}{50}}$$ = $$12 imesfrac{50}{8}=75$$ km/hr => Ans - (A)