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22/10/2021 7:15 pm
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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?
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22/10/2021 7:23 pm
Total distance = 200 km
Average speed = 70 km/h
Total time taken = \(\frac{Total\;distance}{Average\;speed}\)
= \(\frac{200}{70}\) = \(\frac{20}{7}\)h
For first part of the journey,
Distance = 100 km
Speed = 50 km/h
Time taken, t1 = \(\frac{100}{50}\) = 2h
For second part of the journey,
Distance = 100 km
Speed = x km/h
Time taken, t2 = \(\frac{100}{x}\)h
t1 + t2 = \(\frac{20}{7}\)
2 + \(\frac{100}{x}\) = \(\frac{20}{7}\)
= \(\frac{100}{x}\) = \(\frac{6}{7}\)
700 = 6x
x = 116.6 km/h