# On a 60 km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast must the train travel the next 30 km so that the average speed is 40 km/h for the entire trip?

$\\ \text{Let the speed of the train for next}\ 30 \mathrm{km} be "x". since, t=\frac{d}{s}\\ So, time taken by the train for first 30 \mathrm{km} t_{1}=\frac{30 k m}{30 k m / h}=1 h \\ Time taken by the train to travel next 30 \mathrm{km} t_{2}=\frac{30 \mathrm{km}}{x \mathrm{km} / \mathrm{h}}=(30 / x) h \\ Time taken for the entire trip: t=\frac{60 k m}{4 k m / h}=1.5 h \\ \mathrm{So}, 1+\frac{30}{x}=1.5 \Rightarrow x=60 \mathrm{km} / \mathrm{h}$

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