A migrant while returning from Mumbai to his home town Bhopal, travels 300 km to his home partly by train and partly by bus. He takes 4hours if he travels 60 km by train and the remaining by bus. If he travels 100 km by train and remaining by bus, he takes 10 mins longer. Find the speed of the bus and the train Pls answer it...
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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.
December 27, 2019
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Puneetha Spoorthi
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Let the speed of the train be x km/hr and the speed of the bus is y km/hr.
So according to question and using Time=
Speed
Distance
Total distance =300 km
Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,
x
60
+
y
240
=4
and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,
x
100
+
y
200
=4+
60
10
⇒
x
100
+
y
200
=
6
25
Now, let
x
1
=u and
y
1
=v
then 60u+240v=4.............eq1
100u+200v=
6
25
..............eq2
multiply eq1 by 5 and eq2 by 6 we get
300u+1200v=20..........eq3
600u+1200v=25...........eq4
Subtracting eq3 qnd eq4 we get
−300u=−5
u=
300
5
=
60
1
Putting the value of u in eq1 we get
60×
60
1
+240v=4
240v=3
v=
240
3
=
80
1
Now
x
1
=u=
60
1
∴x=60
and
y
1
=v=
80
1
∴y=80
Hence the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.
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