Multiple choice

$P$ and $Q$ are two railways stations which are $560$ km apart. An express train leaves stations $P$ to stations $Q$ at a speed of $55$ km/hr and a passenger train leaves station $Q$ to station $P$ at a speed of $25$ km/hr, both at the same time. Find when and where will the both trains meet.

  1. After $4$ hours at a distance of $325$ km from station $P$
  2. After $7$ hours at a distance of $385$ km from station $P$
  3. After $5$ hours at a distance of $295$ km from station $P$
  4. After $8$ hours at a distance of $345$ km from station $P$
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B Correct answer
Explanation

Relative speed = 55 + 25 = 80 km/hr. Time to meet = Distance / Relative speed = 560 / 80 = 7 hours. Distance from station P = Speed of train P * Time = 55 * 7 = 385 km.

AI explanation

Using the meeting time formula for two objects moving towards each other, divide the total distance by the sum of their speeds: 560 km divided by (55 km/hr plus 25 km/hr) equals 560 divided by 80, giving a meeting time of 7 hours. To find the meeting point distance from station P, multiply the express train's speed by this time: 55 km/hr multiplied by 7 hours equals 385 km. The result is after 7 hours at a distance of 385 km from station P.

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