2017 · Q31
A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m., an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km ?
Elementary MathematicsTime, Speed and Distance
- A4 p.m.
- B2 a.m.
- C12 midnight
- D6 a.m.
Explanation
Let the passenger train's speed be v km/h (express: v+15). Meeting mid-route (540 km each): passenger time t = 540/v, express time t − 3 = 540/(v+15). Then (v+15)(540/v − 3) = 540 gives v² + 15v − 2700 = 0, so v = 45 and t = 12 h. 6 p.m. + 12 hours = 6 a.m.: option D.