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.
Answers
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.