$$\frac{1}{3}$$ part of a certain journey is covered with the speed of 25 km/hr, $$\frac{1}{2}$$ part of the journey is covered with the speed of 45 km/hr and the remaining part covered with the speed of 37.5 km/hr. What is the average speed (in km/h ?->(Show Answer!)

1. $$\frac{1}{3}$$ part of a certain journey is covered with the speed of 25 km/hr, $$\frac{1}{2}$$ part of the journey is covered with the speed of 45 km/hr and the remaining part covered with the speed of 37.5 km/hr. What is the average speed (in km/hr) for the whole journey?

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By: anil on 05 May 2019 03.00 pm

Let total distance covered in the journey be = $$6x$$ km Distance covered with the speed of 25 km/hr = $$frac{1}{3} imes6x=2x$$ km Distance covered with the speed of 45 km/hr = $$frac{1}{2} imes6x=3x$$ km
Thus, remaining distance covered with speed of 37.5 km/hr = $$6x-(2x+3x)=x$$ km Now, total time taken throughout the journey = $$(frac{2x}{25})+(frac{3x}{45})+(frac{x}{37.5})$$ = $$(frac{6x}{75})+(frac{5x}{75})+(frac{2x}{75})=frac{13x}{75}$$ hr
$$ herefore$$ Average speed = total distance / total time = $$6xdivfrac{13x}{75}$$ = $$6x imesfrac{75}{13x}=34.61$$ km/hr => Ans - (B)

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