Roohi travels 600 km to her home partly by train and partly by bus.She takes 8 hours if she travels 120 km by train and the remaining by bus .If she travels 200 km by train and the remaining by bus , she takes 20 minutes longer. Find the speed of the train and the bus separately
Answers
Answer:
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.
Answer:
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.