Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

# Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

1. A
60 km/hr and 80 km/hr
2. B
20 km/hr and 30 km/hr
3. C
30 km/hr and 30 km/hr
4. D
80 km/hr and 60 km/hr

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### Solution:

Given that, Total distance covered by Roohi to reach home is 300 km.
Let the speed of the train be x km/hr and the speed of the bus is y km/hr.
According to question and using Time=Thus, Total distance =300 km.
Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,
Then,100 km by train, 300−100=200 by bus, and takes 10 minutes more,
Now, let Multiply eq1 by 5 and eq2 by 6 we get,
Subtracting eq3 and eq4 we get,
Putting the value of u in eq1 we get:
Now,
Hence, the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.

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