Math, asked by yashwanth2079, 4 months ago

36. Ved travels 600km to his house partly by train and partly by car. He takes 8
hours if he travels 120km by train and the rest by car. He takes 20 min
longer if he travels 200km by train and the rest by car. Find the speed of the
train and the car.​

Answers

Answered by eshatailor19
1

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.

I hope this helps you

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