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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 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. Correct Answer 220 km

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

Concept used:

Distance = Speed × 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, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.

Calculation:

Train from station B towards station A started after 45 minutes of train from station A

Speed of train from station A = 80 km/hr

For 45 minutes it runs alone

⇒ Distance covered in 45 mins = 80 × 45/60 = 60 km

Total distance = 400 km

⇒ Distance remaining = 400 – 60 = 340 km

Now, when the two objects are moving in opposite directions, relative speed is computed by adding the two speeds

So, 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 hours

Now, distance covered by train from station A in 2 hours = (80 × 2) = 160 km

So, Total distance at which they will meet from A = (160 + 60) km

⇒ Distance from station A at which both trains meet = 220 km

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