Question

IN
7. Ramesh travels 760 km to his home partly by train and partly
hours if he travels 160 km. by train and the rest by car. He takes
the travels 240 km by train and the rest by car. Find the speed
respectively.​

Answer 1

Let the speed of train be xkm/hr

and the speed car be ykm/hr respectively.

We know that Speed=

Time

Distance

⇒Time=

Speed

Distance

In Case 1

Distance travelled by train = 160km

Distance travelled by car = (760-160)km = 600km

Time taken by train+Time taken by car = 8 hours

Hence the equation becomes

x

160

+

y

600

=8

In case 2

Distance travelled by train = 240km

Distance travelled by car = (760-240)km = 520km

Time taken by train+Time taken by car = 8 hours+12 minutes

Hence the equation becomes

x

240

+

y

520

=

5

41

......(2)

Hence we get two equations

x

160

+

y

600

=8.........(1)

x

240

+

y

520

=

5

41

......(2)

Let

x

1

=pand

y

1

=q

Hence we get equations

160p + 600q = 8........(3)

240p + 520q = 41/5...(4)

Solving equations (3) and (4)we get p=1/80 and q =1/100

Hencep=

x

1

⇒x=

p

1

=80

Similaryy=

q

1

=100

Solving we get x = 80 and y = 100

hence, speed of train =80km/hr and speed of car =100km/hr.