PLEASE SOLVE ANYONE THIS SUM
Answers
Answer:
ved goes by train = 120 km
" " ". car = 600-120= 480km
total time = 8 hr
If he goes 200km by train take 20 min extra
i.e (200-120) km = 80km travel in 20 minutes by train
then the speed of the train = 80 / 20 km/min = 4 km /min = 240 km/hr
i.e 240 km travel in 1 hr by train
120 km travel in 120/240 hr = 1/2 hr
ved travels by car 480 km in ( 8hr -1/2hr) = 7 hr 30m = 450min
i.e speed of the car = 480/ 450 km /min = 16/15× 60 km /hr = 64 km/hr
Step-by-step explanation:
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/hr.