A man covers a certain distance by train. Had the train moved 14 km/hr faster, it would have taken 35 minutes less. If it moved 10 km/hr slower, it would have taken 30 minutes more. Find the distance covered by the train during the journey.
780 km
Let original speed be v km/h and distance be D. Using the two given conditions and solving the resulting equations simultaneously:
\(\dfrac{v+14}{24} = \dfrac{v-10}{20}\) leads to \(20(v+14) = 24(v-10) \Rightarrow 520 = 4v \Rightarrow v = 130\) km/h.
Original time: \(T = \dfrac{v-10}{20} = \dfrac{120}{20} = 6\) hours.
Distance: \(D = vT = 130\times6 = 780\) km.
Hence, the distance covered by the train is 780 km.
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