The distance between 2 stations Delhi & Lucknow is 500 km. A train starts at…
2024
The distance between 2 stations Delhi & Lucknow is 500 km. A train starts at 5.00 pm from Delhi and moves towards Lucknow at an average speed of 50 km/hrs. Another train starts at 4.20 pm and moves towards Delhi at an average speed of 70 km/hr. How far from Delhi the two trains meet and in how much time ?
- A.
184.5 km, 4.245 hrs
- B.
188.9 km, 3.778 hrs
- C.
188.9 km, 3.778 hrs
- D.
188.9 km, 3.778 hrs
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
To solve this, we must align the start times of the two trains and then calculate their meeting point.
Synchronize start times:
Delhi train starts at 5:00 PM.
Lucknow train starts at 4:20 PM.
The Lucknow train has a 40-minute (2/3 of an hour) head start.
In 40 minutes, the Lucknow train covers: Speed * Time = 70 km/h * (2/3) h = 140/3 km ≈ 46.67 km.
Calculate remaining distance:
Total distance = 500 km.
Distance remaining at 5:00 PM = 500 - 46.67 = 453.33 km.
Calculate relative speed:
Since they move towards each other, relative speed = 50 + 70 = 120 km/h.
Calculate time to meet after 5:00 PM:
Time = Remaining distance / Relative speed = 453.33 / 120 ≈ 3.778 hours.
Calculate distance from Delhi:
The Delhi train travels for 3.778 hours at 50 km/h.
Distance from Delhi = 50 * 3.778 ≈ 188.9 km.