(Q13).Formulate the following problems as a pair of equations and then find their solutions.

(ii) Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car.

Let the speed of the train be x kmph

and the speed of the car = y kmph

By problem,

x
 +
y
 = ⇒
x
 +
y
 =
x
 +
y
 = +
⇒
x
 +
y
 =
⇒
x
 +
y
 =
Take
1
x
 = and
1
y
 = , then

the given equations reduce to

a + b = 1 ……… (1)

a + b =
1
3
 ⇒ a + b = 1 ……… (2)
equation (1) × ⇒ a + b =
equation (2) × ⇒ a + b =
-a = -
⇒ a =
-
-
 =
Substituting a =
1
 in equation (1) we get
15 (
1
 ) + 60b = 1 ⇒
1
 + 60b = 1
⇒ 60b = 1 -
1
 =
⇒ b =
× 60
 =
but a =
1
x
 =
1
 ⇒ x = kmph
b =
1
y
 =
1
 ⇒ y = kmph

Speed of the train = kmph and

speed of the car = kmph