The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey ?

For first $100\ km$:

$Distance_1=100\ km$

$Speed_1=50\ km/h$

Therefore, $Time_1=\frac{Distance_1}{Speed_1}=\frac{100\ km}{50\ km/h}=2\ h$

For Second $100\ km$:

$Distance_2=100\ km$

$Time_2=\frac{100}{Speed_2}$

As given that the average speed$=70\ km/h$

And we know that, average speed$=\frac{total\ distance}{total\ time}$

Therefore, $70=\frac{100+100}{2+\frac{100}{Speed_2}}$

Or $70(2+\frac{100}{Speed_2})=200$

Or $140+\frac{7000}{Speed_2}=200$

Or $\frac{7000}{Speed_2}=200-140$

Or $\frac{7000}{Speed_2)=60$

Or $Speed_2=\frac{7000}{60}$

Or $Speed_2=116.6\ km/h$

Therefore, for the train should travel at the speed of $116.6\ km/h$.

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Updated on: 10-Oct-2022

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