Q11 A man travels 600 km to his home partly by train and partly by car. He takes & hrs, ik he
travels 120 km by train and rest by car. He takes 20 mins ionger if he travels 200 km by frain
and rest by car. Find the speed of train and the car.
Answers
Answer:
Let the speed of the train be x km/hr and the speed of the car be y km/hr.
Case I: When he travels 120 km by train and the rest by car.
If Ved travels 120km by train, then
Distance covered by car is (600−120)km=480km.
Now, Time taken to cover 120km by train =
x
120
hrs. [∵Time=
Speed
Distance
]
Time taken to cover 480 km by car =
y
480
hrs
It is given that the total time of the journey is 8 hours.
∴
x
120
+
y
480
=8
⇒8(
x
15
+
y
60
)=8
⇒
x
15
+
y
60
=1
⇒
x
15
+
y
60
−1=0 ..(i)
Case II When he travels 200 km by train and the rest by car
If Ved travels 200km by train, then
Distance travelled by car is (600−200)km=400km
Now, Time taken to cover 200km by train =
x
200
hrs
Time taken to cover 400 km by train =
y
400
hrs
In this case the total time of journey is 8 hour 20 minutes.
∴
x
200
+
y
400
=8hrs 20 minutes
⇒
x
200
+
y
400
=8
3
1
[∵8hrs20minutes=8
60
20
hrs=8
3
1
hrs]
⇒
x
200
+
y
400
=
3
25
⇒25(
x
8
+
y
16
)=
3
25
⇒
x
8
+
y
16
=
3
1
⇒
x
24
+
y
48
=1
⇒
x
24
+
y
48
−1=0 .(ii)
Putting
x
1
=u and
y
1
=v in equations (i) and (ii), we get
15u+60v−1=0 (iii)
24u+48v−1=0 ..(iv)
By using cross-multiplication, we have
60×−1−48×−1
u
=
15×−1−24×−1
−v
=
15×48−24×60
1
⇒
−60+48
u
=
−15+24
−v
=
720−1440
1
⇒
−12
u
=
−9
v
=
−720
1
⇒u=
−720
−12
=
60
1
and v=
−720
−9
=
80
1
Now, u=
x
1
⇒
60
1
=
x
1
⇒x=60
and, v=
y
1
⇒
80
1
=
y
1
⇒y=80
Hence, the speed of a train is 60 km/hr and the speed of a car is 80 km/hrs