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 its important..
Answers
Answered by
2
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.
Answered by
0
Let the speed of train and bus be u km/h and v km/h respectively.
According to the question,
....(i)
....(ii)
Let
The given equations reduce to:
60p + 240q = 4 ....(iii)
100p + 200q =
600p + 1200q = 25....(iv)
Multiplying equation (iii) by 10, we obtain:
600p + 2400q = 40....(v)
Subtracting equation (iv) from equation (v), we obtain:
1200q = 15
q =
Substituting the value of q in equation (iii), we obtain:
60p + 3 = 4
60p = 1
p =
:. p = , q =
u = 60 km/h , v = 80 km/h
Thus, the speed of train and the speed of bus are 60 km/h and 80 km/h respectively.
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