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The distance between two cities P and Q is 300km. A train starts from station P at 10 am with speed 80 km/hr towards Q. Another train starts from Q towards P with speed 40km/hr at 11 am. At what time do they meet.
- a)12: 50 pm
- b)1 pm
- c)12: 20 pm
- d)12: 40 pm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The distance between two cities P and Q is 300km. A train starts from ...
First train starts at 10 am so in one hour it covers 80 km in one hour. Now distance b/w P and Q is 220. Suppose at some’ x’ km they meet. So,
x/80 = (220-x)/40
x = 440/3.
The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
Therefore, they will meet at 12: 50 pm
x/80 = (220-x)/40
x = 440/3.
The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
Therefore, they will meet at 12: 50 pm
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Community Answer
The distance between two cities P and Q is 300km. A train starts from ...
Distance Between Cities
- The distance between cities P and Q is 300 km.
Train Departure Times and Speeds
- Train from P:
- Starts at 10 am
- Speed = 80 km/hr
- Train from Q:
- Starts at 11 am
- Speed = 40 km/hr
Time Calculation Before Meeting
- By the time the second train starts at 11 am, the first train has already traveled for 1 hour.
- Distance covered by Train P in 1 hour = Speed × Time = 80 km/hr × 1 hr = 80 km.
- Remaining distance between the two trains when the second train starts = 300 km - 80 km = 220 km.
Relative Speed of the Two Trains
- The two trains are now moving towards each other.
- Combined speed = Speed of Train P + Speed of Train Q = 80 km/hr + 40 km/hr = 120 km/hr.
Time to Meet After 11 am
- Time taken to cover the remaining distance of 220 km = Distance / Relative Speed = 220 km / 120 km/hr = 1.833 hours (or 1 hour and 50 minutes).
Final Meeting Time
- Since the second train starts at 11 am, adding 1 hour and 50 minutes gives:
- 11:00 am + 1 hour 50 minutes = 12:50 pm.
Thus, the two trains will meet at 12:50 pm, which corresponds to option (a).
- The distance between cities P and Q is 300 km.
Train Departure Times and Speeds
- Train from P:
- Starts at 10 am
- Speed = 80 km/hr
- Train from Q:
- Starts at 11 am
- Speed = 40 km/hr
Time Calculation Before Meeting
- By the time the second train starts at 11 am, the first train has already traveled for 1 hour.
- Distance covered by Train P in 1 hour = Speed × Time = 80 km/hr × 1 hr = 80 km.
- Remaining distance between the two trains when the second train starts = 300 km - 80 km = 220 km.
Relative Speed of the Two Trains
- The two trains are now moving towards each other.
- Combined speed = Speed of Train P + Speed of Train Q = 80 km/hr + 40 km/hr = 120 km/hr.
Time to Meet After 11 am
- Time taken to cover the remaining distance of 220 km = Distance / Relative Speed = 220 km / 120 km/hr = 1.833 hours (or 1 hour and 50 minutes).
Final Meeting Time
- Since the second train starts at 11 am, adding 1 hour and 50 minutes gives:
- 11:00 am + 1 hour 50 minutes = 12:50 pm.
Thus, the two trains will meet at 12:50 pm, which corresponds to option (a).
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