Two trains A and B leave Delhi for Hyderabad at 7:00 a.m. and 7:50 a.m. on the same day and travel at 80 kmph and 100 kmph respectively. After how many kilometers from Delhi will the two trains be together?

Explanation

Train A leaves 50 minutes (or \frac{5}{6} hours) earlier than Train B. Distance covered by Train A in this time = 80 \times \frac{5}{6} = \frac{200}{3} km. The relative speed of Train B with respect to Train A is 100 - 80 = 20 km/h. Time taken for B to catch A = \frac{\text{Distance head start}}{\text{Relative Speed}} = \frac{200/3}{20} = \frac{10}{3} hours. Distance from Delhi when they meet = \text{Speed of B} \times \text{Time} = 100 \times \frac{10}{3} = \frac{1000}{3} km.

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