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A train started from station A and preceded towards station B at a speed of 80 km/hr 45 minutes later, another train started from station B towards A at the speed of 90 km/hr. If the distance between station A and Station B is 400 km. Find the distance at which both trains meet from A-
- a)160 km
- b)180 km
- c)220 km
- d)240 km
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A train started from station A and preceded towards station B at a sp...
Given data:
- Speed of train from A to B = 80 km/hr
- Speed of train from B to A = 90 km/hr
- Time delay for the second train to start = 45 minutes = 45/60 = 0.75 hours
- Distance between station A and station B = 400 km
To find: The distance at which both trains meet from station A
Let's assume that both trains meet at a distance x km from station A.
Calculating the time taken by the first train to reach the meeting point:
- Speed = Distance/Time
- Time = Distance/Speed
- Time taken by the first train = x/80
Calculating the time taken by the second train to reach the meeting point:
- Time taken by the second train = (x + 400)/90
(Note: The second train has to cover the entire distance of 400 km and travel an additional distance x km to reach the meeting point)
Since the second train started 45 minutes later, the total time taken by the second train would be the time taken by the first train plus the time delay:
- Time taken by the second train = x/80 + 0.75
Setting up the equation:
x/80 + 0.75 = (x + 400)/90
Simplifying the equation:
90x + 7200 = 80x + 32000
10x = 24800
x = 24800/10
x = 2480 km
Answer:
Therefore, the distance at which both trains meet from station A is 2480 km, which is option (c) in the given options.
- Speed of train from A to B = 80 km/hr
- Speed of train from B to A = 90 km/hr
- Time delay for the second train to start = 45 minutes = 45/60 = 0.75 hours
- Distance between station A and station B = 400 km
To find: The distance at which both trains meet from station A
Let's assume that both trains meet at a distance x km from station A.
Calculating the time taken by the first train to reach the meeting point:
- Speed = Distance/Time
- Time = Distance/Speed
- Time taken by the first train = x/80
Calculating the time taken by the second train to reach the meeting point:
- Time taken by the second train = (x + 400)/90
(Note: The second train has to cover the entire distance of 400 km and travel an additional distance x km to reach the meeting point)
Since the second train started 45 minutes later, the total time taken by the second train would be the time taken by the first train plus the time delay:
- Time taken by the second train = x/80 + 0.75
Setting up the equation:
x/80 + 0.75 = (x + 400)/90
Simplifying the equation:
90x + 7200 = 80x + 32000
10x = 24800
x = 24800/10
x = 2480 km
Answer:
Therefore, the distance at which both trains meet from station A is 2480 km, which is option (c) in the given options.
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Community Answer
A train started from station A and preceded towards station B at a sp...
Given,
Speed of train starting from station A = 80 km/hr
Train from station B started after 45 minutes at the speed of 90 km/hr
Distance between station A and station B = 400 km
Distance = Speed x Time
Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, the relative speed is calculated as their difference. When the two objects are moving in opposite directions, the relative speed is computed by adding the two speeds.
Train from station B towards station A started after 45 minutes of the train from station A
Speed of train from station A = 80 km/hr
For 45 minutes it runs alone,
⇒ Distance covered in 45 minutes
Total distance =400 km
⇒ Distance remaining = 400 − 60 = 340 km
Now, when the two objects are moving in opposite directions, the relative speed is computed by adding the two speeds relative speed = (80 + 90)
⇒ Relative speed = 170 km/hr
⇒ Time taken to cover remaining distance = 340/170 = 2 hours
So, they will meet after 2 hr
Now, distance covered by train from station A in 2 hr = (80 × 2) = 160 km
Therefore, Total distance at which they will meet from A = (160 + 60) km
⇒ Distance from station A at which both trains meet = 220 km.
Hence, the correct option is (C).
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A train started from station A and preceded towards station B at a speed of 80 km/hr 45 minutes later, another train started from station B towards A at the speed of 90 km/hr. If the distance between station A and Station B is 400 km. Find the distance at which both trains meet from A-a)160 kmb)180 kmc)220 kmd)240 kmCorrect answer is option 'C'. Can you explain this answer?
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