Two trains start at the same time from stations P and Q and travel towards each other at the speeds of 75 km/h and 100 km/h, respectively. When they meet, it is found that one train has travelled 50 km more than the other. The distance (in km) between two stations is:
- A300
- B350
- C375
- D325
Solution & Step-by-step Explanation
Let the time taken by both trains to meet be t hours.
Distance travelled by the first train from P: D
1
=75t
Distance travelled by the second train from Q: D
2
=100t
The difference in distance travelled by the two trains is given as 50 km:
D
2
−D
1
=50
100t−75t=50
25t=50⟹t=2 hours
The total distance between stations P and Q is the sum of the distances covered by both trains:
Total Distance=D
1
+D
2
=75t+100t=175t
Total Distance=175×2=350 km
Distance travelled by the first train from P: D
1
=75t
Distance travelled by the second train from Q: D
2
=100t
The difference in distance travelled by the two trains is given as 50 km:
D
2
−D
1
=50
100t−75t=50
25t=50⟹t=2 hours
The total distance between stations P and Q is the sum of the distances covered by both trains:
Total Distance=D
1
+D
2
=75t+100t=175t
Total Distance=175×2=350 km